Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Open in App

Solution

Resolving into prime factors:

$252 = 2 \times 2 \times 3 \times 3 \times 7$

Thus, the given number must be multiplied by 7 to get a perfect square.

New number = $252 \times 7 = 1764$

∴ $\sqrt{1764} = 2 \times 3 \times 7 = 42$

Suggest Corrections

Similar questions

Q. Find the smallest number by which

252

must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Q. For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square numbers so obtained.

252

Q. Find the smallest number by which

300

must be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square so obtained.

Question 5 (i)
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

252

Q. By what smallest number must

180

be multiplied so that it becomes a perfect square? Also, find the square root of the number so obtained.

Join BYJU'S Learning Program

Find the smallest number by which 252 must be multiplied to get a perfect square. Also, find the square root of the perfect square so obtained.

Resolving into prime factors:252=2×2×3×3×7Thus, the given number must be multiplied by 7 to get a perfect square.New number = 252×7=1764∴1764=2×3×7=42

Resolving into prime factors:

$252 = 2 \times 2 \times 3 \times 3 \times 7$

Thus, the given number must be multiplied by 7 to get a perfect square.

New number = $252 \times 7 = 1764$

∴ $\sqrt{1764} = 2 \times 3 \times 7 = 42$