Square - Simplify From Squared Factors, Values and Variables, Radical Remaining (Level 2)

This math topic focuses on simplifying radicals involving squared factors, values, and variables. It includes detailed practice problems that require extracting and simplifying squared factors from under the radical sign while leaving the non-squared parts inside the radical. Each problem presents an expression involving variables and constants under a radical, and students must identify the correct simplification with multiplicative constants and variable parts in and out of the radical. The problems progressively integrate more complex algebraic expressions, enhancing understanding of simplifying square roots and radicals.

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

more
View

Radicals - Square - Simplify From Squared Factors, Values and Variables, Radical Remaining Worksheet

Mobius Math Academy logo
Radicals - Square - Simplify From Squared Factors, Values and Variables, Radical Remaining
1
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 3 times d to the power of 2 times d to the power of 2 times d
a A LaTex expression showing 5{d} to the power of 2 square root of 5d
b A LaTex expression showing {d} to the power of 4 square root of {d to the power of 3 }
c A LaTex expression showing 7dsquare root of {d to the power of 2 }
d A LaTex expression showing 4{d} to the power of 2 square root of 3d
e A LaTex expression showing {d} to the power of 3 square root of d
2
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 11 times b to the power of 2 times b to the power of 2 times b
a A LaTex expression showing 4{b} to the power of 2 square root of 11b
b A LaTex expression showing 2bsquare root of 14{b to the power of 2 }
c A LaTex expression showing 2{b} to the power of 3 square root of 11b
d A LaTex expression showing 6bsquare root of 7b
e A LaTex expression showing 2{b} to the power of 3 square root of 12b
3
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 5 times b to the power of 2 times b
a A LaTex expression showing 6{b} to the power of 3 square root of 6{b to the power of 2 }
b A LaTex expression showing 5bsquare root of 8b
c A LaTex expression showing 5bsquare root of 5b
d A LaTex expression showing 5{b} to the power of 3 square root of 7b
e A LaTex expression showing 4bsquare root of 3b
4
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 11 times n to the power of 2 times n
a A LaTex expression showing 5nsquare root of 11n
b A LaTex expression showing 3nsquare root of 14{n to the power of 3 }
c A LaTex expression showing 8{n} to the power of 3 square root of 11n
d A LaTex expression showing {n} to the power of 3 square root of 13{n to the power of 3 }
e A LaTex expression showing 8nsquare root of 7{n to the power of 2 }
5
Simplify the radical
A LaTex expression showing square root of 2 times 3 to the power of 2 times b to the power of 2 times b to the power of 2
a A LaTex expression showing 5b
b A LaTex expression showing 3{b} to the power of 2 square root of 2
c A LaTex expression showing 4{b} to the power of 3 square root of 4
d A LaTex expression showing 2{b} to the power of 4 square root of 5
e A LaTex expression showing {b} to the power of 3
6
Simplify the radical
A LaTex expression showing square root of 5 to the power of 2 times 5 times c to the power of 2 times c
a A LaTex expression showing 6csquare root of 4{c to the power of 2 }
b A LaTex expression showing 5csquare root of 5c
c A LaTex expression showing 5csquare root of 6c
d A LaTex expression showing 7csquare root of 2{c to the power of 3 }
e A LaTex expression showing csquare root of 4{c to the power of 3 }
7
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 times b
a A LaTex expression showing 4square root of {b to the power of 3 }
b A LaTex expression showing 2square root of 2b
c A LaTex expression showing 3square root of 3b
d A LaTex expression showing 2square root of {b to the power of 3 }
e A LaTex expression showing square root of b
8
Simplify the radical
A LaTex expression showing square root of 2 to the power of 2 times 2 to the power of 2 times 7 times y
a A LaTex expression showing 6square root of 9{y to the power of 3 }
b A LaTex expression showing 4square root of 7y
c A LaTex expression showing 5square root of 7{y to the power of 2 }
d A LaTex expression showing 2square root of 6{y to the power of 3 }
e A LaTex expression showing 4square root of 8{y to the power of 2 }