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

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

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.

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

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

• 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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