Simplifying radicals activity involves the process of solving radicals equation with step by step solution. Activity is the process of solving equations with radicals symbol. The square root symbol is also represented as radicals. Simplifying radicals is easily carried out by performing squaring operations on the given equation is known as simplifying radicals activity. The following are the example problems which explain the radicals activity.
In logarithm, the radical pictogram is represented by √. The symbol n√x , n, x and √ are represented by index , radical and and radical symbol. Steps to multiplying radicals is the similar way of ordinary multiplications, additionally it has the following conditions. When multiplying two or more radicals, we must multiply the numbers exterior radicals and then multiply the numbers in the interior radicals.
Steps to multiplying radicals:
The following steps to multiplying radicals, when the radicals have the indistinguishable key, n:
Step 1: Utilize the multiplying radicals rule for nth roots to find the product of the radicals.
Step 2: Simplify the product by factoring and taking the nth root of the factors that are ideal nth powers.
Rules on multiplying radicals:
The following rules for steps to multiplying radicals helps the easy way of understanding and simplifying the radical expression.
Rule 1:
n√x . n√y = n√(x . y)
Rule 2:
n√( x + y) . n√(x – y) = n√(x2 – y2)
Rule 3:
(x. n √y)n = xn . y
Simplifying Radicals Activity Example Problems:
Ex:1 Solve the radicals.
`sqrt(u^2-5u+7) = 1`
Sol:
Given equation is
`sqrt(u^2-5u+7) = 1`
To solve the radical symbol perform squaring operation on both sides
`[sqrt(u^2-5u+7)]^2 = (1)^2`
And simplify.
u 2 – 5u+7= 1
Make the above equation in factor form.
u 2 - 5 u + 6 = 0
The above equation is in quadratic equation form with two solutions
u = 3 and u = 2 is the answer.
Ex:2 Solve the radicals.
`sqrt(3u-5) = u - 1`
Sol:
Given equation is
`sqrt(3u-5) = u - 1`
To solve the radical symbol perform squaring operation on both sides
`[sqrt( 3u-5)]^2 = (u-1)^2`
Simplify the above equation
3 u - 5 = u 2 - 2 u + 1
Change the above equation in factor form.
u 2 - 5 u + 6 = 0
The above equation is in quadratic equation form with two solutions
u = 2 and u = 3 is the answer.
Ex:3 Solve the radicals.
`sqrt(u^2-16u+37) = 3`
Sol:
Given equation is
`sqrt(u^2-16u+37) = 3`
To solve the radical symbol perform squaring operation on both sides
`[sqrt(u^2-16u+37)]^2 = (3)^2`
And simplify.
u 2 – 16u+37= 9
Make the above equation in factor form.
u 2 - 16 u + 28 = 0
The above equation is in quadratic equation form with two solutions
u = 2 and u = 14 is the answer.
Practice Problems on Simplifying Radicals:
Q:1 Solve the radicals.
` sqrt(u^2-12u+29) = 3`
Answer: u = 2 and u = 10.
Q:2 Solve the radicals.
`sqrt(4u-3) = u -2`
Answer: u = 7 and u = 1
Multiplying Radicals:
Ex:1 (a) Steps to multiplying radicals √2 . √36.
Sol:
1. Multiply the i nside radical numbers : = √(2 .36) = √72
2. Simplify radicals if possible : = √(2 . 62 )
3. Answer : = 6 √2
(b) Steps to multiplying radicals √5 . √7
Sol:
1. Multiply the inside radical numbers = √(5 . 7)
2. Simplify radicals if possible = √35
(c) Steps to multiplying radicals 4√7 . 7√5
Sol:
1. Multiply the outside of radical numbers first (4 . 7) = 28
2. Multiply the inside radical numbers √(7 . 5) = √35
3. . Put steps 1 and 2 together 28√35
4. Answer 28√35
Ex:2 (a) Steps to multiplying radicals √(4 + 6) . √(4 - 6)
Sol:
√(4 + 6) . √(4 - 6) (given)
= √(42 – 62)
= √(16 – 36)
= √-20 (Simplify radicals if possible )
= 2√-5 (Answer)
(b) Steps to multiplying radicals √(3 + 2) . √(3 - 2)
Sol:
√(3 + 2) . √(3 - 2) (given)
= √(32 – 22)
= √(9 -4) (Simplify radicals if possible )
= √5 (Answer)
Examples on rule:
(a) Steps to multiplying radicals (7√3)2
Sol:
(7√3)2 (given)
= 72 . 3
= 49 . 3
= 147 (Answer)
(b) Steps to multiplying radicals (3√2)2
Sol:
(3√2)2 (given)
= 32 . 2
= 9 . 2
= 18 (Answer)
In logarithm, the radical pictogram is represented by √. The symbol n√x , n, x and √ are represented by index , radical and and radical symbol. Steps to multiplying radicals is the similar way of ordinary multiplications, additionally it has the following conditions. When multiplying two or more radicals, we must multiply the numbers exterior radicals and then multiply the numbers in the interior radicals.
Steps to multiplying radicals:
The following steps to multiplying radicals, when the radicals have the indistinguishable key, n:
Step 1: Utilize the multiplying radicals rule for nth roots to find the product of the radicals.
Step 2: Simplify the product by factoring and taking the nth root of the factors that are ideal nth powers.
Rules on multiplying radicals:
The following rules for steps to multiplying radicals helps the easy way of understanding and simplifying the radical expression.
Rule 1:
n√x . n√y = n√(x . y)
Rule 2:
n√( x + y) . n√(x – y) = n√(x2 – y2)
Rule 3:
(x. n √y)n = xn . y
Simplifying Radicals Activity Example Problems:
Ex:1 Solve the radicals.
`sqrt(u^2-5u+7) = 1`
Sol:
Given equation is
`sqrt(u^2-5u+7) = 1`
To solve the radical symbol perform squaring operation on both sides
`[sqrt(u^2-5u+7)]^2 = (1)^2`
And simplify.
u 2 – 5u+7= 1
Make the above equation in factor form.
u 2 - 5 u + 6 = 0
The above equation is in quadratic equation form with two solutions
u = 3 and u = 2 is the answer.
Ex:2 Solve the radicals.
`sqrt(3u-5) = u - 1`
Sol:
Given equation is
`sqrt(3u-5) = u - 1`
To solve the radical symbol perform squaring operation on both sides
`[sqrt( 3u-5)]^2 = (u-1)^2`
Simplify the above equation
3 u - 5 = u 2 - 2 u + 1
Change the above equation in factor form.
u 2 - 5 u + 6 = 0
The above equation is in quadratic equation form with two solutions
u = 2 and u = 3 is the answer.
Ex:3 Solve the radicals.
`sqrt(u^2-16u+37) = 3`
Sol:
Given equation is
`sqrt(u^2-16u+37) = 3`
To solve the radical symbol perform squaring operation on both sides
`[sqrt(u^2-16u+37)]^2 = (3)^2`
And simplify.
u 2 – 16u+37= 9
Make the above equation in factor form.
u 2 - 16 u + 28 = 0
The above equation is in quadratic equation form with two solutions
u = 2 and u = 14 is the answer.
Practice Problems on Simplifying Radicals:
Q:1 Solve the radicals.
` sqrt(u^2-12u+29) = 3`
Answer: u = 2 and u = 10.
Q:2 Solve the radicals.
`sqrt(4u-3) = u -2`
Answer: u = 7 and u = 1
Multiplying Radicals:
Ex:1 (a) Steps to multiplying radicals √2 . √36.
Sol:
1. Multiply the i nside radical numbers : = √(2 .36) = √72
2. Simplify radicals if possible : = √(2 . 62 )
3. Answer : = 6 √2
(b) Steps to multiplying radicals √5 . √7
Sol:
1. Multiply the inside radical numbers = √(5 . 7)
2. Simplify radicals if possible = √35
(c) Steps to multiplying radicals 4√7 . 7√5
Sol:
1. Multiply the outside of radical numbers first (4 . 7) = 28
2. Multiply the inside radical numbers √(7 . 5) = √35
3. . Put steps 1 and 2 together 28√35
4. Answer 28√35
Ex:2 (a) Steps to multiplying radicals √(4 + 6) . √(4 - 6)
Sol:
√(4 + 6) . √(4 - 6) (given)
= √(42 – 62)
= √(16 – 36)
= √-20 (Simplify radicals if possible )
= 2√-5 (Answer)
(b) Steps to multiplying radicals √(3 + 2) . √(3 - 2)
Sol:
√(3 + 2) . √(3 - 2) (given)
= √(32 – 22)
= √(9 -4) (Simplify radicals if possible )
= √5 (Answer)
Examples on rule:
(a) Steps to multiplying radicals (7√3)2
Sol:
(7√3)2 (given)
= 72 . 3
= 49 . 3
= 147 (Answer)
(b) Steps to multiplying radicals (3√2)2
Sol:
(3√2)2 (given)
= 32 . 2
= 9 . 2
= 18 (Answer)
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