How do you simplify #(11y)/sqrt3#?

Question

Hazel Anglin · Accepted Answer

#(11ysqrt(3))/3#

The simplification required is to remove the root from the denominator of the fraction (so that roots are confined to the numerator).

This may be achieved by multiplying by #1# (so that the value of the overall expression is unchanged), but choosing an appropriately constructed expression that evaluates to #1# (noting that anything divided by itself (excluding zero) equals #1#).

The specially chosen instance of #1# requires a number in its denominator that will remove the root. This can be achieved by multiplying by something divided by #sqrt(3)#, as #sqrt(3) xx sqrt(3) = 3#. To ensure the complete number is #1#, the numerator must also have #sqrt(3)#.

So, the required simplification is

#(11y)/sqrt(3) xx sqrt(3)/sqrt(3)#

#(11ysqrt(3))/3#

Julia Adams · Answer

#(11y)/sqrt3 = (11y sqrt3)/3# Simplify by rationalizing the denominator: #(11y)/sqrt3 xx sqrt3/sqrt3# #= (11yxx sqrt3)/(sqrt3)^2# #= (11y sqrt3)/3#

Isaiah Anthony · Answer

undefined To simplify (11y)/sqrt3, you can multiply both the numerator and denominator by sqrt3. This will eliminate the square root in the denominator. The simplified form is (11y * sqrt3) / 3.