Question

3. Is 180 a perfect square? If not, then with what least number should it be multiplied, so that it becomes
a perfect square? What would be the square root of this new number?
​

Answer 1

Answer:

180 is not perfect square.It should be multiplied by least no. 5 to get perfect square. √900=30.20

Answer 2

Given:

• Is 180 a perfect square? If not, then with what least number should it be multiplied, so that it becomes a perfect square? What would be the square root of this new number?

Solution:

180 is not a perfect as it has odd number of zeros at the end.

By Prime Factorisation method,

• 180 = 2 × 2 × 3 × 3 × 5

The prime factors 2 and 3 are in pairs. But the prime factor 5 is not in pairs.

∴⠀⠀5 should be multiplied with 180, so that it becomes a perfect square.

• 180 × 5 = 900

So, now, we need to find the square root of 900.

By Prime Factorisation method,

$\\ \sf \: \: \: \: \: \: \: 900 = 2 \times 2 \: \times 3\times 3 \times 5 \times 5 \\ \\ \\ \sf \therefore \: \sqrt{900} \: \: = { \sqrt{ \underline{2 \times 2} \times {\underline{3 \times3 }}\times { \underline{5 \times 5 } } }} \\ \\ \\ \sf = 2 \times3 \times 5 \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \purple { \pmb{ \underline{Hence, \: The \: square \: root \: of \: 900 \: = \: 30 \: }}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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$\: \: \: \: \: \: \sf \: \underline{Hope \: it \: helps \: !! } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \underline { \sf \: Stay \: home \: ! \: Stay \: safe }\: ! \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$