How would you simplify sqrt48 + sqrt3?

4 Answers
Feb 13, 2016

5sqrt3

Explanation:

We can split up sqrt48 using the rule that sqrt(ab)=sqrtasqrtb.

Thus, sqrt48=sqrt(16*3)=sqrt16sqrt3=4sqrt3.

The original expression can be rewritten as

4sqrt3+sqrt3=sqrt3(4+1)=5sqrt3

Feb 13, 2016

Short story, try watching the result of division of the two numbers and substitute it in the bigger one.

sqrt(48)+sqrt(3)=5sqrt(3)

Explanation:

Always try reducing the high number to something of which you know the root. Here someone should notice that:

48/3=16<=>48=3*16

The root of 16 is known, while the root of 3 can be factored. Therefore:

sqrt(48)+sqrt(3)

sqrt(16*3)+sqrt(3)

sqrt(16)*sqrt(3)+sqrt(3)

4*sqrt(3)+sqrt(3)

5sqrt(3)

Feb 13, 2016

5sqrt3

Explanation:

radicals in simplified form are asqrtb
where a is a rational number.

to begin with , simplify sqrt48

by considering the factors of 48 , particularly 'squares'

the factors required here are 16 (square) and 3.

using the following : sqrta xx sqrtb hArr sqrtab

sqrt48 = sqrt16 xx sqrt3 = 4sqrt3

hence sqrt48 + sqrt3 = 4sqrt3 + sqrt3 = 5sqrt3

Feb 13, 2016

color(blue)(5sqrt3)

:)

Explanation:

To simplify radicals, we must find first its largest "perfect squares" that evenly divides to simplify.

Since, sqrt(ab) = sqrta*sqrtb (Theorem)

sqrt48 + sqrt 3

PerfectSquares:

color(blue)(4) = 2*2
color(blue)(9) = 3*3
color(blue)(16) = 4*4
color(blue)(25) = 5*5
color(blue)(36) = 6*6
color(blue)(49) = 7*7
color(blue)(64) = 8*8
color(blue)(81) = 9*9
color(blue)(100) = 10*10

we can simplify sqrt48, as 48 evenly divides with 16,

we get,

sqrt48 = sqrt(16*3)

using theorem from above,

sqrt48 = sqrt(16)*sqrt(3)

simplify,

sqrt48 = 4*sqrt3

=4sqrt3

since the rule of radical signs is just like variables we can combine like terms, with a slight difference.

asqrtb+-asqrtb=(a+a)sqrtb

4sqrt3 + sqrt3

4sqrt3 + (1)sqrt3

color(blue)(= 5sqrt3)