Question

find the smallest number by which the following numbers should be divided to obtain a perfect square. also find the square root of the perfect square thus obtained: 4563​

Answer 1

Step-by-step explanation:

Solution:

(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=636=2×3=6



(ii) 2925 = 3 x 3 x 5 x 5 x 13

Here, prime factor 13 has no pair. Therefore 2925 must be divided by 13 to make it a perfect square.

\therefore2925\div13=225∴2925÷13=225

And \sqrt{225}=3\times5=15225=3×5=15



(iii) 396 = 2 x 2 x 3 x 3 x 11

Here, prime factor 11 has no pair. Therefore 396 must be divided by 11 to make it a perfect square.

\therefore396\div11=36∴396÷11=36

And \sqrt{36}=2\times3=636=2×3=6



(iv) 2645 = 5 x 23 x 23

Here, prime factor 5 has no pair. Therefore 2645 must be divided by 5 to make it a perfect square.

\therefore2645\div5=529∴2645÷5=529

And \sqrt{529}=23529=23



(v) 2800 = 2 x 2 x 2 x 2 x 5 x 5 x 7

Here, prime factor 7 has no pair. Therefore 2800 must be divided by 7 to make it a perfect square.

\therefore2800\div7=400∴2800÷7=400

And \sqrt{400}=2\times2\times5=20400=2×2×5=20



(vi) 1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5

Here, prime factor 5 has no pair. Therefore 1620 must be divided by 5 to make it a perfect square.

\therefore1620\div5=324∴1620÷5=324

And \sqrt{324}=2\times3\times3=18324=2×3×3=18