Question

Find the square root of the following: $196a^6{b}^8{c}^{10}$

• A. $14a^3{b}^4{c}^5$
• B. $14a^2{b}^4{c}^5$
• C. $14a^3{b}^3{c}^5$
• D. None of these

Answer 1

The correct option is A $14a^3{b}^4{c}^5$

We find the square root of $196a^6{b}^8{c}^{10}$ as shown below:

$=\sqrt{196a^6{b}^8{c}^{10}}$

$=\sqrt{196\times a^6\times b^8\times c^{10}}$

$=\sqrt{(2\times 2\times 7\times 7)\times (a^3{)}^2\times (b^4{)}^2\times (c^5{)}^2}$

$=\sqrt{(2^2\times 7^2)\times (a^3{)}^2\times (b^4{)}^2\times (c^5{)}^2}$

$=\sqrt{(14{)}^2\times (a^3{)}^2\times (b^4{)}^2\times (c^5{)}^2}$

$=\sqrt{(14a^3{b}^4{c}^5{)}^2}$

$=14a^3{b}^4{c}^5$

Hence, the square root of $196a^6{b}^8{c}^{10}$ is $14a^3{b}^4{c}^5$.