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.

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

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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) over Fraction (Level 2)'. Part of a broader unit on 'Radicals - Multiplication Intro' Learn online: app.mobius.academy/math/units/radicals_multiplication_intro/
1
A LaTex expression showing \frac{square root of 48{c to the power of 3 } times square root of 75{c to the power of 2 }}{2 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 135{c} to the power of 2 square root of c
b A LaTex expression showing 90{c} to the power of 2 square root of c
c A LaTex expression showing 60{c} to the power of 2 square root of c
d A LaTex expression showing 135csquare root of c
e A LaTex expression showing {c} to the power of 2 square root of c
2
A LaTex expression showing \frac{square root of 45c times square root of 80}{3 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 60square root of c
b A LaTex expression showing 80square root of c
c A LaTex expression showing 106
d A LaTex expression showing 60csquare root of c
3
A LaTex expression showing \frac{square root of 12{b to the power of 4 } times square root of 48{b to the power of 4 }}{3 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 10{b} to the power of 4
b A LaTex expression showing 16{b} to the power of 4
c A LaTex expression showing 24{b} to the power of 3
d A LaTex expression showing 24{b} to the power of 5
4
A LaTex expression showing \frac{square root of 20 times square root of 45{z to the power of 3 }}{3 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 30zsquare root of z
b A LaTex expression showing 20zsquare root of z
c A LaTex expression showing 13z
d A LaTex expression showing 13zsquare root of z
e A LaTex expression showing 30{z} to the power of 2
5
A LaTex expression showing \frac{square root of 12x times square root of 75{x to the power of 2 }}{5 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 18xsquare root of x
b A LaTex expression showing 30xsquare root of x
c A LaTex expression showing xsquare root of x
d A LaTex expression showing 120xsquare root of x
6
A LaTex expression showing \frac{square root of 28{r to the power of 2 } times square root of 112{r to the power of 3 }}{7 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4{r} to the power of 2 square root of r
b A LaTex expression showing 56{r} to the power of 3
c A LaTex expression showing 16{r} to the power of 2 square root of r
d A LaTex expression showing 56{r} to the power of 2
7
A LaTex expression showing \frac{square root of 12{b to the power of 3 } times square root of 48}{2 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 24{b} to the power of 2
b A LaTex expression showing 48bsquare root of b
c A LaTex expression showing 24{b} to the power of 2 square root of b
d A LaTex expression showing 24b
e A LaTex expression showing 96bsquare root of b