Question

5. For each of the following numbers, find the smallest whole number by which be multiplied so as to get a perfect square number. Also find the square me square number so obtained. (i) 252 (ii) 180 (iii) 1008 (v) 1458 (vi) 768 (iv) 22.​

Answer 1

Answer:

(i) 252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.

\therefore252\times7=1764∴252×7=1764

And (i) 

$\sqrt{1764} =2\times3\times7=421764=2×3×7=42</p><p>$

(ii) 180 = 2 x 2 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

\therefore180\times5=900∴180×5=900

And,

$\sqrt{900}=2\times3\times5=30900=2×3×5=30$

(iii) 1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

\therefore1008\times7=7056∴1008×7=7056

And 

$\sqrt{7056}=2\times2\times3\times7=847056=2×2×3×7=84$

(iv) 2028 = 2 x 2 x 3 x 13 x 13

Here, prime factor 3 has no pair. Therefore 2028 must be multiplied by 3 to make it a perfect square.

\therefore2028\times3=6084∴2028×3=6084

And 

$\sqrt{6084}=2\times2\times3\times3\times13\times13=786084$

=2×2×3×3×13×13=78

or baki khud se bana lo

Answer 2

Answer:

this is the solution

Step-by-step explanation:

(i) 252 = 2 x 2 x 3 x 3 x 7

Here, prime factor 7 has no pair. Therefore 252 must be divided by 7 to make it a perfect square.

\therefore252\div7=36∴252÷7=36

And \sqrt{36}=2\times3=6  

36

​

=2×3=6