# Perfect Squares

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**Procedure to check whether a given natural number is a perfect squares or not.**

**Step I :**Obtain the natural number.

**Step II :**Write the number as a product of prime factors.

**Step III :**Group the factors in pairs in such a way that both the factors in each pair are equal.

**Step IV:**See whether some factor is left over or not. If no factor is left over in the grouping, then the given number is a perfect square. Otherwise, it is not a perfect-square.

**Step V:**To obtain the number whose square is the given number taken over one factor from each group and multiply them.

**Examples on perfect-square**

1) Is 225 a perfect-square? If so, find the number whose square is 225.

**Solution :**

Resolving 225 into prime factors, we obtain

225 = 3 x 3 x 5 x 5

Grouping the factors in pairs in such a way that both the factors in each pair are equal, we have

225 = ( 3 x 3 ) x ( 5 x 5 )

Clearly, 225 can be grouped into pairs of equal factors and no factor is left over.

Hence, 225 is a perfect-square.

Again, 225 = (3 x 5) x (3 x 5)

= 15 x 15 = 15

^{2}

So, 225 is the square of 15.

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2) Is 150 a perfect-square? If so,find the number whose square is 150.

**Solution :**

Resolving 150 into prime factors, we obtain

150 = 2 x 3 x 5 x 5

Grouping the factors in pairs in such a way that both the factors in each pair are equal, we have

225 = 2 x 3 x ( 5 x 5 )

Clearly, 150 can be grouped into pairs of equal factors.2 and 3 factors are left over.

Hence, 150 is not a perfect-square.

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**Practice Problems**

**Q.1**Check whether the following numbers are perfect- squares or not, give reason.

1) 250 2) 289 3) 1024 4) 1156 5) 1000

**Q.2**The following numbers are perfect-squares,find whose perfect-squares are those.

1) 2 x 3 x 3 x 2 x 5 x 5

2) 7 x 7 x 2 x 11 x 2 x 11

3) 2 x 3 x 3 x 2 x 7 x 7

**Squares and Square roots**

• Introduction of Squares and Square Roots

• Perfect Squares or not

• Properties of Square Numbers

• Short cut method to find squares

• Introduction of Square Roots

• Properties of Square Roots

• Square root by Prime factorization method

• Square root by long division method

• Square root of rational numbers

• Square root of Decimals

• Square root by estimation method

• Introduction of Squares and Square Roots

• Perfect Squares or not

• Properties of Square Numbers

• Short cut method to find squares

• Introduction of Square Roots

• Properties of Square Roots

• Square root by Prime factorization method

• Square root by long division method

• Square root of rational numbers

• Square root of Decimals

• Square root by estimation method

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