Roots of Real Numbers and Radicals
Questions with Solutions for Grade 10
Grade 10 questions on roots of numbers and radicals with solutions are presented.
Definition
x is the n^{th} root of a number y is equivalent to x^{n} = y.
For n = 2, the n^{th} root is called the square root.
For n = 3, the n^{th} root is called the cubic root.
Examples
1) Since 3^{2} = 9, 3 is the square (n=2) root of 9.
2) Also since (3)^{2} = 9, 3 is also a square root of 9.
3) Since (2)^{3} = 8, 2 is the cubic (n = 3) root of 8
4) Since 3^{4} = 81 and (3)^{4} =81, the fourth roots of $81$ are $3$ and $3$
Properties of Roots of Real Numbers
1) For n even and y positive, there are two n^{th} roots of y
Examples
Since 10^{4}=10000 and (10)^{4} = 10000, the fourth roots of 10000 are 10 and 10.
2) For n even and y negative, there are no real n^{th} roots of y.
Examples
The square root of  4 is not a real number since no real number x exists such that x^{2} = 4
The fourth root of  16 is not a real number since no real number x exists such that x^{4} = 16
3) For n odd, there is always one n^{th} root of y.
Examples
The cubic (n=3) root of 8 is equal to 2.
The fifth root (n=5) of 100000 is equal to 10
Principal Root
For n even, the principal root is the positive root. For n odd there is only one root and it is the principal root.
Examples
The principal 6^{th} of 64 is equal to 2.
The principal cubic root of 64 is equal to  4.
Radical Notation
The symbol √ is called a radical and is used to indicate the principal root of a number as follows:
^{n}√y
where n is called the index of the radical and y is called the radicand.
Examples
Because of its widespread use, the square root of y is written as √y without indicating the index.
Questions With Answers
18.
Use a calculator to approximate the following to 3 decimal places:
Solutions to the Above Problems


More High School Math (Grades 10, 11 and 12)  Free Questions and Problems With Answers
More Middle School Math (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
More Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers
Author 
email
Home Page