Question

Find the smallest number to multiply with 150 to make it a perfect square

Answer 1

FIRST DO PRIME FACTORIZATION OF 150.
THEN MAKE PAIR OF SAME NUMBERS.
THE WHICH WILL GET UNPAIRED WILL BE THE NUMBER WE HAVE TO MULTIPLY.

Answer 2

$\textbf{Explaination :}$
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“Look at the number 150. It is not a perfect square because it has a single zero in it's unit digit.”

“According to the question, as the number 150 is not a perfect square. Inorder to make it a perfect square we need to multiply it with a certain number to convert it into a perfect square”

$\textbf{Solution :}$
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$\textbf{Note :}$ We are doing it by prime factorisation method.

“So, we need to find the prime factors of 150”

Prime Factors of 150
= 5 × 5 × 2 × 3

“Have a look at the factors, we need to pair them out. So, only 5 is in pair but 2 and 3 are not in pair. So, we will take them in the next step.”

Smallest number to be multiplied
= 2 × 3
= 6

Perfect Sq.

$= \sqrt{ 150 \times 6 }= \sqrt{5 \times 5 \times 2 \times 3 \times 6} \\ \\ = \sqrt{900} \: \: \: \: \: \: \: \: = \sqrt{5 \times 5 \times 6 \times 6} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5 \times 6 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 30$

•°• The perfect sq. is 900

$\sqrt{900} = 30$

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