Home > Algebra > Addition and Subtraction of Radicals

How do you simplify #(4sqrt32) /3 +( 5sqrt18) / 6#?

Answer 1

Eli Assouline

#color(brown)((47sqrt2)/6#

#(4sqrt32)/3+(5sqrt18)/6#

By calculator#color(brown)(=11.07800624#

#:.=(8sqrt32+5sqrt18)/6#

#:.=(8 xx sqrt(4*4*2)+5sqrt(3*3*2))/6#

#sqrt4 xx sqrt4=4,sqrt3 xx sqrt3=3#

#:.=(8 xx 4sqrt(2)+5 xx 3sqrt(2))/6#

#:.=(32sqrt(2)+15sqrt(2))/6#

#:.color(brown)(=(47sqrt2)/6# by calculator #color(brown)(=11.07800624#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Jace Anderson

To simplify the expression (4√32)/3 + (5√18)/6, we can simplify the square roots and then combine like terms.

First, we simplify the square roots: √32 = √(16 * 2) = 4√2 √18 = √(9 * 2) = 3√2

Now, we substitute these simplified square roots back into the expression: (4√32)/3 + (5√18)/6 = (4 * 4√2)/3 + (5 * 3√2)/6

Next, we simplify the fractions: (16√2)/3 + (15√2)/6 = (16√2)/3 + (15√2)/6

To combine the fractions, we need a common denominator, which is 6: (16√2)/3 + (15√2)/6 = (32√2)/6 + (15√2)/6

Now, we can add the fractions: (32√2 + 15√2)/6 = (47√2)/6

Therefore, the simplified expression is (47√2)/6.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.