**Square Root of Fractions and Decimals Worksheet :**

Worksheet given in this section will be much useful for the students who would like to practice problems on finding square root of fractions and decimals.

Before look at the worksheet, if you would like to know, how to find square root of fractions and decimals,

**Problem 1 : **

Find the square root of 4/9.

**Problem 2 : **

Find the square root of 169/289.

**Problem 3 : **

Find the square root of 2.56.

**Problem 4 : **

Find the square root of 51.84.

**Problem 5 : **

Find the square root of 0.2916.

**Problem 1 : **

Find the square root of 4/9.

**Solution : **

√(4/9) = √4 / √9

When we decompose 4 and 9 into prime factors, we get

4 = 2^{2}

9 = 3^{2}

Then, we have

√(4/9) = √2^{2} / √3^{2}

√(4/9) = 2/3

So, the square root of 4/9 is 2/3.

**Problem 2 : **

Find the square root of 169/289.

**Solution : **

√(169) = √169 / √289

When we decompose 169 and 289 into prime factors, we get

169 = 13^{2}

289 = 17^{2}

Then, we have

√(169/289) = √13^{2} / √17^{2}

√(169/289) = 13/17

So, the square root of 169/289 is 13/17.

**Problem 3 : **

Find the square root of 2.56.

**Solution : **

Convert the decimal number 2.56 into a fraction.

Because there are two digits after the decimal point, multiply and divide 2.56 by 100 to get rid of the decimal point.

2.56 = (2.56 ⋅ 100) / 100

2.56 = 256 / 100

Take square root on each side.

√2.56 = √(256/100)

Take square separately for numerator and denominator.

√2.56 = √256 / √100 -----(1)

To find the square root of 256 and 100, decompose 256 and 100 into prime factors using synthetic division as shown below.

From the above synthetic division, we have

256 = 2^{8}

100 = 2^{2} ⋅ 5^{2}

Then, we have

(1)-----> √2.56 = √2^{8} / √(2^{2} ⋅ 5^{2})

√2.56 = 2^{4} / (2 ⋅ 5)

√2.56 = 16 / 10

√2.56 = 1.6

So, the square root of 2.56 is 1.6.

**Problem 4 : **

Find the square root of 51.84.

**Solution : **

Convert the decimal number 51.84 into a fraction.

Because there are two digits after the decimal point, multiply and divide 51.84 by 100 to get rid of the decimal point.

51.84 = (51.84 ⋅ 100) / 100

51.84 = 5184 / 100

Take square root on each side.

√51.84 = √(5184/100)

Take square separately for numerator and denominator.

√51.84 = √5184 / √100 -----(1)

To find the square root of 5184 and 100, decompose 5184 and 100 into prime factors using synthetic division as shown below.

From the above synthetic division, we have

5184 = 2^{6} ⋅ 3^{4}

100 = 2^{2} ⋅ 5^{2}

Then, we have

(1)-----> √51.84 = √(2^{6} ⋅ 3^{4}) / √(2^{2} ⋅ 5^{2})

√51.84 = (2^{3} ⋅ 3^{2}) / (2 ⋅ 5)

√51.84 = (8 ⋅ 9) / 10

√51.84 = 72/10

√51.84 = 7.2

So, the square root of 51.84 is 7.2.

**Problem 5 : **

Find the square root of 0.2916.

**Solution : **

Convert the decimal number 0.2916 into a fraction.

Because there are four digits after the decimal point, multiply and divide 0.2916 by 10000 to get rid of the decimal point.

0.2916 = (0.2916 ⋅ 10000) / 10000

0.2916 = 2916 / 10000

Take square root on each side.

√0.2916 = √(2916/10000)

Take square separately for numerator and denominator.

√0.2916 = √2916 / √10000 -----(1)

To find the square root of 2916 and 10000, decompose 2916 and 10000 into prime factors using synthetic division as shown below.

From the above synthetic division, we have

2916 = 2^{2} ⋅ 3^{6}

10000 = 5^{4} ⋅ 2^{4}

Then, we have

(1)-----> √0.2916 = √(2^{2} ⋅ 3^{6}) / √(5^{4} ⋅ 2^{4})

√0.2916 = √(2^{2} ⋅ 3^{6}) / √(5^{4} ⋅ 2^{4})

√0.2916 = (2 ⋅ 3^{3}) / (5^{2} ⋅ 2^{2})

√0.2916 = (2 ⋅ 27) / (25 ⋅ 4)

√0.2916 = 54/100

√0.2916 = 0.54

So, the square root of 0.2916 is 0.54.

After having gone through the stuff given above, we hope that the students would have understood, how to find square root of fractions and decimals.

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