Radicals

Multiplying Monomials (Values and Variables) over Fraction (Level 2)

This topic focuses on the multiplication and simplification of radical expressions involving monomials (both values and variables), particularly when these expressions are divided by fractional coefficients. It introduces learners to efficiently combining and simplifying expressions under radical signs alongside dealing with fractional division. The problems ask students to multiply radicals containing variables raised to powers and subsequently simplify the expressions for a result in simplest radical form. The practice involves recognizing patterns in radicals, manipulating exponents, and understanding fractional ratios in the context of radical expressions. The content forms part of an introductory series on radical multiplication.

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

more

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

Mobius Math Academy logo
Radicals - Multiplying Monomials (Values and Variables) over Fraction
1
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 32{q to the power of 2 } times square root of 50{q to the power of 3 }}{5 over 3 }
a A LaTex expression showing 40{q} to the power of 3 square root of q
b A LaTex expression showing 14{q} to the power of 3
c A LaTex expression showing 40{q} to the power of 3
d A LaTex expression showing 14{q} to the power of 2
e A LaTex expression showing 24{q} to the power of 2 square root of q
2
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 28{n to the power of 2 } times square root of 63}{7 over 5 }
a A LaTex expression showing 42n
b A LaTex expression showing 42{n} to the power of 2
c A LaTex expression showing 30n
d A LaTex expression showing 21
3
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 27z times square root of 48{z to the power of 4 }
a A LaTex expression showing {z} to the power of 2 square root of z
b A LaTex expression showing 36{z} to the power of 3
c A LaTex expression showing 180{z} to the power of 2 square root of z
d A LaTex expression showing 36{z} to the power of 3 square root of z
e A LaTex expression showing 36{z} to the power of 2 square root of z
4
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 50 times square root of 18{p to the power of 2 }}{3 over 2 }
a A LaTex expression showing 30square root of p
b A LaTex expression showing 30{p} to the power of 2
c A LaTex expression showing 30psquare root of p
d A LaTex expression showing 13p
e A LaTex expression showing 20p
5
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 8{y to the power of 3 } times square root of 50}{5 over 2 }
a A LaTex expression showing 3ysquare root of y
b A LaTex expression showing 20ysquare root of y
c A LaTex expression showing 20{y} to the power of 2
d A LaTex expression showing ysquare root of y
e A LaTex expression showing 8ysquare root of y
6
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 32r times square root of 8r
a A LaTex expression showing 16square root of r
b A LaTex expression showing 16r
c A LaTex expression showing 16{r} to the power of 2
d A LaTex expression showing 48r
7
Multiply the radical expressions and simplify the answer
A LaTex expression showing square root of 80 times square root of 45{w to the power of 4 }
a A LaTex expression showing 60{w} to the power of 2
b A LaTex expression showing 60w
c A LaTex expression showing 60{w} to the power of 2 square root of w
d A LaTex expression showing 60wsquare root of w
8
Multiply the radical expressions and simplify the answer
A LaTex expression showing \frac{square root of 45z times square root of 80{z to the power of 2 }}{2 over 3 }
a A LaTex expression showing 180zsquare root of z
b A LaTex expression showing 60square root of z
c A LaTex expression showing 120zsquare root of z
d A LaTex expression showing 60zsquare root of z
e A LaTex expression showing 90zsquare root of z