Question

4 root 7 minus 3 root 252 + 5 root 343

Answer 1

Given:

4 root 7 minus 3 root 252 + 5 root 343

To find:

Simplify the given problem

Solution:

We will now solve the given problem step by step, which is as follows:

$4\sqrt{7} \:-\:3\sqrt{252} \: + \:5\sqrt{343}$

we will find the factors of terms inside the root

= $4\sqrt{7} \:-[\:3\sqrt{2\:\times\:2\:\times\:3\:\times\:3\:\times\:7} \:] + [\:5\sqrt{7\:\times\:7\:\times\:7}]$

we will now take the common pairs outside the root

= $4\sqrt{7} \:-[\:3\:\times\:2\:\times\:3\:\times\:\sqrt{7} \:] + [\:5\:\times\:7\:\times\:\sqrt{7}]$

= $4\sqrt{7} \:-[\:18\:\times\:\sqrt{7} \:] + [\:35\:\times\:\sqrt{7}]$

= $4\sqrt{7} \:-\:18\sqrt{7} \: +\:\:35\sqrt{7}$

now according to the rule of VBODMAS, we will do the addition then the subtraction

= $[4\sqrt{7} +\:\:35\sqrt{7}] \:-\:18\sqrt{7} \:$

= $39\sqrt{7} \:-\: 18\sqrt{7}$

= $\bold{21\sqrt{7}}$

Thus, the final answer is $\underline{21\sqrt{7}}$.

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