Multiplying Monomials (Values and Variables) over Unit Fraction (Level 1)

This math topic focuses on practicing the multiplication of monomials involving radicals (square roots), where the products are divided by unit fractions. The problems involve variables with algebraic expressions under radical signs and require simplification after the operations. Each question presents multiple choices for the simplified result, reinforcing the concepts of manipulating and simplifying radicals, managing powers of variables, and handling fractions within radical expressions.

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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Math worksheet on 'Radicals - Multiplying Monomials (Values and Variables) over Unit Fraction (Level 1)'. 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 45 times square root of 5{n to the power of 2 }}{1 over 2 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 15n
b A LaTex expression showing 30n
c A LaTex expression showing 60n
d A LaTex expression showing 60nsquare root of n
e A LaTex expression showing 45n
2
A LaTex expression showing \frac{square root of 2{y to the power of 2 } times square root of 8y}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 4ysquare root of y
b A LaTex expression showing 4{y} to the power of 2 square root of y
c A LaTex expression showing 36ysquare root of y
d A LaTex expression showing 12ysquare root of y
3
A LaTex expression showing \frac{square root of 32{y to the power of 3 } times square root of 2y}{1 over 4 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 8ysquare root of y
b A LaTex expression showing 8y
c A LaTex expression showing 24{y} to the power of 2
d A LaTex expression showing 8{y} to the power of 2
e A LaTex expression showing 32{y} to the power of 2
4
A LaTex expression showing \frac{square root of 11{d to the power of 4 } times square root of 176{d to the power of 3 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 44{d} to the power of 4
b A LaTex expression showing 220{d} to the power of 3 square root of d
c A LaTex expression showing 176{d} to the power of 3 square root of d
d A LaTex expression showing 44{d} to the power of 3 square root of d
5
A LaTex expression showing \frac{square root of 3{p to the power of 4 } times square root of 27{p to the power of 4 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 9{p} to the power of 4
b A LaTex expression showing 9{p} to the power of 3
c A LaTex expression showing 9{p} to the power of 4 square root of p
d A LaTex expression showing 45{p} to the power of 4
e A LaTex expression showing {p} to the power of 4
6
A LaTex expression showing \frac{square root of 3 times square root of 27{m to the power of 4 }}{1 over 3 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 9{m} to the power of 3
b A LaTex expression showing 27{m} to the power of 2
c A LaTex expression showing 9{m} to the power of 2
7
A LaTex expression showing \frac{square root of 3{x to the power of 4 } times square root of 27{x to the power of 2 }}{1 over 5 }
Multiply the radical expressions and simplify the answer
a A LaTex expression showing 9{x} to the power of 2 square root of x
b A LaTex expression showing 45{x} to the power of 3
c A LaTex expression showing 9{x} to the power of 3 square root of x
d A LaTex expression showing 9{x} to the power of 4