Question

Find the square root of:
$121(x-a{)}^4(x-b{)}^6(x-c{)}^{12}$

• A. $11|(x-a{)}^2(x-b{)}^3(x-c{)}^6|$
• B. $11|(x-a{)}^3(x-b{)}^3(x-c{)}^6|$
• C. $11|(x-a{)}^2(x-b{)}^4(x-c{)}^6|$
• D. None of these

Answer 1

Answer: (A)

$11|(x-a{)}^2(x-b{)}^3(x-c{)}^6|$

We find the square root of $121(x-a{)}^4(x-b{)}^6(x-c{)}^{12}$ as shown below:

$\sqrt{121(x-a{)}^4(x-b{)}^6(x-c{)}^{12}}=\sqrt{{11}^2\times \left[\right(x-a{)}^2{]}^2\times \left[\right(x-b{)}^3{]}^2\times \left[\right(x-c{)}^6{]}^2}=\sqrt{\left[11\right(x-a{)}^2(x-b{)}^3(x-c{)}^6{]}^2}=11\left|\right(x-a{)}^2(x-b{)}^3(x-c{)}^6|$

Hence, the square root of $121(x-a{)}^4(x-b{)}^6(x-c{)}^{12}$ is $11\left|\right(x-a{)}^2(x-b{)}^3(x-c{)}^6|$.