Question

1.)by which leat number should 243 be multiplied so that it is a perfect square? Find the perfect square number.Also,find the square root.​

Answer 1

Answer:

Step-by-step explanation:

We have 243 = 3 × 3 × 3 × 3 × 3

The prime factor 3 is not a group of three.  

∴ 243 is not a perfect cube.      

Now, [243] × 3 = [3 × 3 × 3 × 3 × 3] × 3    

or 729 =3 × 3 × 3 × 3 × 3 × 3  

Now, 729 becomes a perfect cube.    

Thus, the smallest required number to multiply 243 to make it a perfect cube is 3.

Answer 2

Here,

$243 = \underline{ 3 \times 3} \times \underline{ 3 \times 3}\times 3$

• Two pairs has been formed but one 3's is left unpaired, so another 3 must be added as multiplicand.

Thus,

• New obtained number = 3 × 243 = 729

Now,

$\text{Square Root of 729} = \sqrt{729} = \green{27}$

Hence,

• Required number which must be multiplied to 243 = 3
• Perfect Square Number = 729
• Square Root of New obtained number = 27