SIMPLIFY RADICALS BY FINDING PERFECT SQUARE FACTORS

Simplify each expression by factoring to find perfect squares and then taking their root.

Problem 1 :

√75

Solution :

Find the perfect square factor of 75.

= √75

= √(25×3)

= √(5×5×3)

= 5√3

So, the answer is 5√3

Problem 2 :

√16

Solution :

Find the factors of 16.

= √16

= √(4×4)

= 4

So, the answer is 4.

Problem 3 :

√36

Solution :

Find the factors of 36.

= √36

= √(6×6)

= 6

So, the answer is 6.

Problem 4 :

√64

Solution :

Find the factors of 64.

= √(8×8)

= 8

So, the answer is 8.

Problem 5 :

√80

Solution :

Find the perfect square factor of 80.

= √80

= √(16×5)

= √(4×4×5)

= 4√5

So, the answer is 4√5.

Problem 6 :

√30

Solution :

We cannot decompose 30 as a product of perfect square, we decompose 30 as

= √(10×3) (or) √(6×5) (or) √(12×5)

We will not get any product of two same terms, so the result is it cannot be simplified further. 

Note : 

To find the exact value, we can use calculator.

Problem 7 :

√8

Solution :

Find the perfect square factor of 8.

= √8

= √(4×2)

= √(2×2×2)

= 2√2

So, the answer is 2√2.

Problem 8 :

√18

Solution :

Find the perfect square factor of 18.

= √18

= √(9×2)

= √(3×3×2)

= 3√2

So, the answer is 3√2.

Problem 9 :

√32

Solution :

Find the perfect square factor of 32.

= √32

= √(16×2)

= √(4×4×2)

= 4√2

So, the answer is 4√2.

Problem 10 :

√12

Solution :

Find the perfect square factor of 12.

= √12

= √(4×3)

= 2√3

So, the answer is 2√3.

Problem 11 :

√108

Solution :

Find the perfect square factor of 108.

= √108

= √(36×3)

= √(6x3×3)

= 6√3

So, the answer is 6√3.

Problem 12 :

√125

Solution :

= √125

= √(25×5)

= √(5x5×5)

= 5√5

So, the answer is 5√5.

Problem 13 :

√50

Solution :

= √50

= √(25×2)

= √(5x5×5)

= 5√2

So, the answer is 5√2.

Problem 14 :

√175

Solution :

= √175

= √(25×7)

= √(5x5×5)

= 5√7

So, the answer is 5√7.