Question

Find square root of$\left( {{x^o} + 5x + 6} \right)\,\,\left( {x + 2} \right)\,\left( {x + 3} \right)$.

Answer 1

Hint: Use the formula and first find out the factors of the quadratic equation and then proceed further

Complete step by step solution: $\left( {{x^2} + 5x + 6} \right)\,\left( {x + 2} \right)\,\left( {x + 3} \right)$ …(i)
Use calculate $\left( {{x^2} + 5x + 6} \right)$.
Product of roots = 6
Sum of roots = 5
Factor of $\left( {{x^2} + 5x + 6} \right)$ is ${x^2} + 2x + 3x + 6$
(use split the value of 5 to make factors)
Now we take the common first two and last two terms.
$x\left( {x + 2} \right) + 3\left( {x + 2} \right)$
Again $\left( {x + 2} \right)$is common.
$\left( {x + 2} \right)\,\left( {x + 3} \right)$ …(ii)
Substitute (ii) in (i) we get
$\left( {{x^2} + 5x + 6} \right)\,\left( {x + 2} \right)\,\left( {x + 3} \right)$
Factors of$\left( {x + 2} \right)\,\left( {x + 3} \right)\,\left( {x + 2} \right)\,\left( {x + 3} \right)$
Now use find square root
$\sqrt {\left( {x + 2} \right)\,\left( {x + 3} \right)\,\left( {x + 2} \right)\,\left( {x + 3} \right)} $
$\left( {x + 2} \right)\,\left( {x + 3} \right)$ ans.


Note: In this type of question we need the factors of solving quadratic equations then we calculate square root.