Question

by what least number 3750 must be multiplied to give a perfect square. Fast tell me it's important​

Answer 1

Answer:

by 6 so that you will get a perfect square of 150 which is 22500

Answer 2

Step-by-step explanation:

Given: $3750$

To find: By what least number 3750 must be multiplied to give a perfect square.

Solution:

Tip:$\bf \sqrt{ {n}^{2} } = n$

Step 1: Write prime factors of 3750

$3750 = 2 \times 3 \times 5 \times 5 \times 5 \times 5$

$3750 = 2 \times 3 \times {5}^{4}$

According to the rule

${5}^{4}$

can be taken out from square root as

${5}^{2}$

But 2 and 3 can not.

Step 2: Multiply by 6

if we Multiply the number by 6, then

$3750 \times 6 = 2 \times 3 \times {5}^{4} \times 2 \times 3$

$3750 \times 6 = {2}^{2} \times {3}^{2} \times {5}^{4}$

Now,

$\sqrt{3750 \times 6} = \sqrt{ {2}^{2} \times {3}^{2} \times {( {5}^{2} )}^{2} }$

$\sqrt{3750 \times 6} = 2 \times 3 \times 25$

$\sqrt{3750 \times 6} = 6 \times 25$

$\bf \sqrt{3750 \times 6} = 150$

Final answer:

If 6 is multiplied by 3750 it will must be a perfect square.

Hope it will help you.

Learn more:

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2) (b) The smallest number by which 1944 should be multiplied so that it becomes a

perfect cube is-

(i)3

(ii) 2

(iii)5

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