Roots of Real Numbers and Radicals
Questions with Solutions
Grade 10 questions on roots of numbers and radicals with solutions are presented.
Definitionx 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. Examples1) 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 Numbers1) For n even and y positive, there are two n^{th} roots of yExamplesSince 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. ExamplesThe square root of  4 is not a real number since no real number x exists such that x^{2} = 4The 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. ExamplesThe cubic (n=3) root of 8 is equal to 2.The fifth root (n=5) of 100000 is equal to 10 Principal RootFor n even, the principal root is the positive root. For n odd there is only one root and it is the principal root.ExamplesThe principal 6^{th} of 64 is equal to 2.The principal cubic root of 64 is equal to  4. Radical NotationThe symbol √ is called a radical and is used to indicate the principal root of a number as follows:where n is called the index of the radical and y is called the radicand. ExamplesBecause 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 References and links
Radical Expressions  Questions with Solutions for Grade 10High School Maths (Grades 10, 11 and 12)  Free Questions and Problems With Answers
Middle School Maths (Grades 6, 7, 8, 9)  Free Questions and Problems With Answers
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