Question

find the least number that is to be multiplied by 2048 to make a perfect square? also find the square root of the new number so obtained?​

Answer 1

Answer:

perfect square 2

Step-by-step explanation:

*We find the prime factors of 2048.

*If 2 gets a pair, then the number will becomes a perfect square. Thus by multiplying the number by 2, we get a perfect square.

*2048 x 2 = 4096 is a perfect square.

*Hence, the required number which is to be multiplied with 2048 to get a perfect square is 2.

Answer 2

Question :

Find the least number that is to be multiplied by 2048 to make a perfect square? also find the square root of the new number so obtained?

Solution :

In order to find the least number firstly we need to do prime factorisation :

$\:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:2048\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:1024 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:512\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:256 \:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:128\:\:}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:64\:\:}}\\\underline{\sf{2}}&{\sf{\:\: \underline{32} \:\:}}{\underline{\sf{}}}& \\{\underline{\sf{2}}}& \underline{\sf{\:\:16\:\:}}\\\underline{\sf{2}}&{\sf{\:\: \underline{8} \:\:}} {\underline{\sf{}}} \\{\underline{\sf{2}}}& \underline{\sf{\:\:4\:\:}}\\\underline{\sf{2}}&{\sf{\:\: \underline{2} \:\:}} {\underline{\sf{}}} \\{\underline{\sf{}}}& \underline{\sf{\:1\:}}\end{array}$

So, the factors are :

$\sf \longrightarrow \sf \: 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Making pairs :

$\sf \longrightarrow \sf \: \underline{2 \times 2} \times \underline{2 \times 2} \times \underline{2 \times 2} \times \underline{2 \times 2 }\times \underline{2 \times 2} \times 2$

We can see that 2 is unpaired.

$\sf \longrightarrow \bf \: 2$

So, 2 should be multiplied. Let's multiply it!!

$\sf \longrightarrow \sf \: 2048 \times 2$

$\sf \longrightarrow \bf \: \underline { 4096}$

Now, finding the square root :

$\sf \longrightarrow \sf \: { \sqrt{4096}}$

$\sf \longrightarrow \bf \: {{ \underline{64}}}$

Hence, the number to be multiplied is 2 and the number is 4096 and thus the square root of the new number so obtained is 64.