Radicals

Multiplying Monomials (Values and Variables) over Unit Fraction (Level 3)

This topic covers the skills of multiplying monomials, which include both values and variables, within the context of working with radicals and unit fractions. It is designed to strengthen understanding of radical expressions, specifically how to multiply and simplify them when placed over a unit fraction. Each question presents a different set of variables and powers, requiring the application of rules for multiplying radicals and simplifying the resulting expressions. This is a more advanced practice in dealing with radicals, aimed at students ready for higher-level algebraic operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction Worksheet

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Radicals - Multiplying Monomials (Values and Variables) over Unit Fra...
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 44z{t to the power of 2 } times square root of 8{z to the power of 2 {t} to the power of 4 }}{1 over 3 }
a A LaTex expression showing 4z{t} to the power of 3 square root of 22z
b A LaTex expression showing 36{t} to the power of 3 square root of 22z
c A LaTex expression showing 36z{t} to the power of 3 square root of z
d A LaTex expression showing 36z{t} to the power of 4 square root of 22z
e A LaTex expression showing 12z{t} to the power of 3 square root of 22z
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 48ny times square root of 75{n to the power of 3 }}{1 over 4 }
a A LaTex expression showing {n} to the power of 2 square root of y
b A LaTex expression showing 60{n} to the power of 2 square root of y
c A LaTex expression showing 960{n} to the power of 2 square root of y
d A LaTex expression showing 240{n} to the power of 2 square root of y
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 80 times square root of 48{r to the power of 3 {t} to the power of 4 }}{1 over 2 }
a A LaTex expression showing 64rtsquare root of 15r
b A LaTex expression showing 64r{t} to the power of 2 square root of 15r
c A LaTex expression showing 64{r} to the power of 2 {t} to the power of 2 square root of 15
d A LaTex expression showing 16r{t} to the power of 2 square root of 15r
e A LaTex expression showing 32r{t} to the power of 2 square root of 15r
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8{p to the power of 2 t} times square root of 52{p to the power of 2 t}}{1 over 2 }
a A LaTex expression showing 16{p} to the power of 2 t
b A LaTex expression showing 4{p} to the power of 2 tsquare root of 26
c A LaTex expression showing {p} to the power of 2 t
d A LaTex expression showing 16{p} to the power of 2 tsquare root of 26
e A LaTex expression showing 8{p} to the power of 2 tsquare root of 26
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 45 times square root of 20{p to the power of 4 m}}{1 over 2 }
a A LaTex expression showing 30{p} to the power of 2 square root of pm
b A LaTex expression showing 120{p} to the power of 2
c A LaTex expression showing 60{p} to the power of 2 square root of m
d A LaTex expression showing 120psquare root of pm
e A LaTex expression showing 30{p} to the power of 3 square root of m
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 20{t to the power of 3 {w} to the power of 3 } times square root of 208{t to the power of 2 {w} to the power of 4 }}{1 over 3 }
a A LaTex expression showing 24{t} to the power of 2 {w} to the power of 3 square root of 65tw
b A LaTex expression showing 8{t} to the power of 2 {w} to the power of 3 square root of 65tw
c A LaTex expression showing 72{t} to the power of 2 {w} to the power of 3 square root of tw
d A LaTex expression showing 32{t} to the power of 2 {w} to the power of 3 square root of 65tw
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 275y times square root of 18t{y to the power of 3 }}{1 over 3 }
a A LaTex expression showing 135{y} to the power of 2 square root of 22yt
b A LaTex expression showing 15{y} to the power of 2 square root of 22yt
c A LaTex expression showing 135{y} to the power of 2 square root of 22t
d A LaTex expression showing 15{y} to the power of 2 tsquare root of 22t
e A LaTex expression showing 45{y} to the power of 2 square root of 22t
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 50{n to the power of 4 } times square root of 12{x to the power of 4 }}{1 over 2 }
a A LaTex expression showing 10{n} to the power of 2 xsquare root of 6
b A LaTex expression showing 40{n} to the power of 2 {x} to the power of 2 square root of 6x
c A LaTex expression showing 20{n} to the power of 2 {x} to the power of 2 square root of 6
d A LaTex expression showing 40{n} to the power of 2 {x} to the power of 2 square root of 6
e A LaTex expression showing 10{n} to the power of 2 {x} to the power of 2