# FIND SQUARE ROOT OF RATIONAL NUMBER

Square root of a number is the factor that we multiply by itself two times to get that number. Consider the following

Here 36 is a perfect square, because we can write 36 as square of 6.

To find a square root of a number, we will follow the steps.

Step 1 :

Decompose the numerator and denominator separately as product of prime factors.

Step 2 :

For every two same values, we can take one out of the square root.

Finding square root of rational number ?

Using the following property, we find square root of rational number.

Evaluate each of the following.

Problem 1 :

√1/25

Solution :

= √1/25

= √1/√25

= √(1  1) / √(5  5)

= 1/5

Problem 2 :

√1/81

Solution :

= √1/81

= √1/√81

= √(1  1)/√(9  9)

= 1/9

Problem 3 :

-√36/144

Solution :

= -√36/144

= -√36/√144

= -√(6  6)/√(12  12)

= -6/12

= -1/2

Problem 4 :

√529/625

Solution :

= √529/625

= √529/√625

= √(23  23)/√(25  25)

= 23/25

Problem 5 :

√16/25

Solution :

= √16/25

= √16/√25

= √(4  4)/√(5  5)

= 4/5

Determine whether each of the following statements in true or false.

Problem 1 :

-√36/324 = 1/3

Solution :

= -√36/324

= -√36/√324

= -√(6⋅6)/√(18⋅18)

= -6/18

= -1/3

So, the statement is false.

Problem 2 :

√324/625 = 18/25

Solution :

= √324/625

= √324/√625

= √(18⋅18)/√(25⋅25)

= 18/25

So, the statement is true.

Problem 3 :

-√900/961 = -30/31

Solution :

= -√900/961

= -√900/√961

= -30/31

So, the statement is true.

Problem 4 :

√1/4 = ± 1/2

Solution :

= √1/4

= √1/√4

= ± 1/2

So, the statement is true.

Problem 5 :

If x/y = -2, find √ (x²/y² + y²/x²)

Solution :

√ (x²/y² + y²/x²) = √ (x/y)² + (y/x)²

= √ (x/y)² + (x/y)-²

= √ (-2)2 + (-2)-2

= √4 + 1/4

= √17/4

= √17/√4

= √17/2

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