Free Mathematics Tutorials

Radical Expressions

Questions with Solutions for Grade 10

Grade 10 questions on how to use some important formuals to simplify radicals algebraic expressions with solutions are presented.

Important Formulas
A) If n and m are positive integers and ⁿ√y is a real number, then
equation 1

Examples
1) √5 is a real number and therefore

2) ³ √(-7) is a real number and therefore
equation 3

B) If n is an EVEN positive integer then
equation 4

Examples

C) If n is an ODD positive integer then
equation 6

Examples

Questions With Answers

Rewrite, if possible, the following expressions without radicals (simplify)

equation 8

Solutions to the Above Problems
equation 9
The index of the radical 3 is odd and equal to the power of the radicand.
equation 10
since √x is a real number, x is positive and therefore |x| = x.
equation 11
equation 12
is not a real number since -x ² - 1 is always negative.
equation 13 .
The index 8 is even and equal to the power of the radicand.
equation 14 .
equation 15 .
equation 16 .
The index 10 of the radical is even and equal to the power of the radicand.
equation 17 .
The index 3 of the radical is odd and equal to the power of the radicand.
equation 18 .
equation 19 .
equation 20
Even index and power of radicand.
equation 21
Even index and power of radicand.