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: 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

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