Question

simplify
$\sqrt{15} ( - \sqrt{3n} + 4n)$
please show all work!​

Answer 1

Answer:

$\displaystyle - 3 \sqrt{5n} + 4 \sqrt{15} n$

Step-by-step explanation:

we would like to simplify the following expression:

$\displaystyle \sqrt{15} ( - \sqrt{3n} + 4n)$

recall distribution property thus:

$\displaystyle - \sqrt{3n} \sqrt{15} + 4n \sqrt{15}$

remember that,

• $\displaystyle \sqrt{a} \sqrt{b} = \sqrt{ab}$

so assign variables:

• $a \implies 3n$
• $b \implies 15$

simplify Multiplication:

$\displaystyle - \sqrt{45n} + 4 \sqrt{15} n$

rewrite 45 as 9×5:

$\displaystyle - \sqrt{9 \times 5n} + 4 \sqrt{15} n$

utilize the formula:

$\displaystyle - \sqrt{9 } \sqrt{5n} + 4 \sqrt{15} n$

simplify square:

$\displaystyle \boxed{- 3 \sqrt{5n} + 4 \sqrt{15} n}$

and we're done!

Answer 2

Laws to be used:-

$\boxed{\sf a(b+c)=ab+bc}$

$\boxed{\sf \sqrt{p}\sqrt{q}=\sqrt{pq}}$

Solution

$\\ \rm\longmapsto \sqrt{15}(-\sqrt{3n}+4n)$

$\\ \rm\longmapsto -\sqrt{15}\sqrt{3n}+4\sqrt{15}n$

$\\ \rm\longmapsto -\sqrt{3(15)n}+4\sqrt{15}n$

$\\ \rm\longmapsto -\sqrt{3(3)(5)n}+4\sqrt{15}n$

$\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{15n}$

Or we can break 15n

$\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{3(5)n}$

$\\ \rm\longmapsto -3\sqrt{5}n+4\sqrt{3}\sqrt{5n}$