How do you simplify 4 sq.root of 75 + sq.root of 27.?

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Answer 1 · 2015-07-13T15:03:13

$4sqrt75+sqrt27=23sqrt3$

We are given:

$4sqrt75+sqrt27$

Let's look at $sqrt75$

$25$ goes into $75$ $3$ times

$3*25=75$

So,

$sqrt75=sqrt(3*25)$

the square root of $25$ is $5$ , so

$sqrt75=sqrt(3*25)=5sqrt3$

Now, let's look at $sqrt27$

$3$ goes into $27$ $9$ times

$3*9=27$

So,

$sqrt27=sqrt(3*9)$

the square root of $9$ is $3$ , so

$sqrt27=sqrt(3*9)=3sqrt3$

So,

$4sqrt75+sqrt27=4*5sqrt3+3sqrt3$

$4*5sqrt3+3sqrt3=20sqrt3+3sqrt3=23sqrt3$

Recall: $asqrtb+csqrtb=(a+c)sqrtb$

Answer 2 · 2015-07-13T15:04:01

$4sqrt(75)+sqrt(27)=23sqrt(3)$

Use $sqrt(ab) = sqrt(a)sqrt(b)$ for $a, b >= 0$

$4sqrt(75)+sqrt(27)$

$=4sqrt(5^2*3)+sqrt(3^2*3)$

$=4sqrt(5^2)sqrt(3)+sqrt(3^2)sqrt(3)$

$=4*5sqrt(3)+3sqrt(3)$

$=20sqrt(3)+3sqrt(3)$

$=23sqrt(3)$