Question

Find the smallest number by which 7350 must be divided to make it a perfect square also find the squre root of the perfect square obatained

Answer 1

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Answer 2

6 is the smallest number by which 7350 must be divided to make it a perfect square

The square root of the perfect square obtained is 35

Solution:

Given that,

We have to find the smallest number by which 7350 must be divided to make it a perfect square

Perfect square: integer that is obtained when a integer is multiplied by itself

Step 1: write prime factorization of 7350

$7350 = 2 \times 3 \times 5 \times 5 \times 7 \times 7$

For a perfect square, each distinct prime factor must occur an even number of times

But here, 2 and 3 occurs only once

Thus,

To get perfect square we must divide by 2 x 3 = 6

$\frac{7350}{6} = 1225$

Thus, 6 is the smallest number by which 7350 must be divided to make it a perfect square

Find the square root of the perfect square obtained

$\sqrt{1225} = \sqrt{5 \times 5 \times 7 \times 7 }\\\\\sqrt{1225} = 5 \times 7 \\\\\sqrt{1225} = 35$

Thus square root of the perfect square obtained is 35

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