Question

Find the smallest number by which 14450 should be multiplied to make it a perfect square. Find the square root of the perfect square soobtained.

Answer 1

Answer:

If we multiple 14,450 with 2 (14450×2) then it will become 28,900. Which is a perfect square.

=√(28,900)

= 170

or,

= 170²

= 28900

Hope it helps............

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Answer 2

➝ 2 must be multiplied to get a perfect square.

Explanation :-

• Take out the L.CM. to get the prime factors

$\bf {\underline{ 2\mid14450}} \\ \bf {\underline{ 5\mid7225 \: \: \: }} \\ \bf \: {\underline{ 5 \mid1445 \: \: \: \: }} \\ \bf \: {\underline{ 17\mid289 \: \: \: \: \: \: \: \: \: \: }} \\ \bf {\underline{ 17\mid17 \: \: \: \: \: \: \: \: \: \: \: }} \\ \bf {{ 1}}$

$\bf \therefore \: </p><p>L.C.M = 2 × { \underline{5 × 5}} × { \underline{17 × 17 }}$

• As observation we can say that "2" is missing.

Hence,

2 must be multiplied...

CHECK POINT :-

• After getting multiplied by 2 we get:-

14,450 × 2 = 28,900

• To verify it we need to take out the root.

Therefore,

= $\bf \sqrt {28900}$

= 170

Hence, proved ...