Examples on Square Root Formulas
Example 1: Find the sum: 5β3 + 6β12
Solution:
5β3 + 6β12
= 5β3 + 6(β(4 Γ 3)
= 5β3 + 6 Γ β4 Γ β3
= 5β3 + 6 Γ2β3
= 5β3 + 12β3 = 17β3
Example 2: Evaluate: β64 β β25
Solution:
β64 β β25
= β(8 Γ 8) β β(5 Γ 5 )
= 8 β 5 = 3
Example 3: Evaluate: β63 / β28
Solution:
β63 / β28
= β(7 Γ 9 )/ β(7 Γ 4 )
= β[(7 Γ 9 )/ (7 Γ 4 )]
= β(9 /4)
= β9 / β4 = 3/2
Example 4: Evaluate: 5 /β15
Solution:
5 /β15
= (5 /β15)Γ(β15 /β15 )
= (5β15)/15
= (β15)/3
Example 5: Evaluate: 4 / (5 + β6)
Solution:
4 / (5 + β6)
= [4 / (5 + β6)] Γ [(5 β β6) / (5 β β6)]
Above step is rationalizing denominator by multiplying by [(5 β β6) / (5 β β6)]
= [4Γ(5 β β6)] / [(5 + β6)Γ (5 β β6)]
= [4Γ(5 β β6)] / [52 β (β6)2]
= (20 β 4β6) / (25 β (β6 Γ β6)]
= (20 β 4β6) / (25 β 6)
= (20 β 4β6) / 19
Example 6: Evaluate : 7 / (8 β β10)
Solution:
7 / (8 β β10)
= [7 / (8 β β10)] Γ [(8 + β10) / (8 + β10)]
Above step is rationalizing denominator by multiplying by [(8 + β10) / (8 + β10)]
= [7Γ(8 + β10)] / [(8 β β10) Γ (8 + β10)]
= [7Γ(8 + β10)] / [82 β (β10)2]
= (56 + 7β10) / (64 β (β10 Γ β10)]
= (56 + 7β10) / (64 β 10)
= (56 + 7β10) / 54
Example 7: Evaluate : (2 +β5) / (4 β β2)
Solution:
(2 +β5) / (4 β β2)
= [(2 +β5) / (4 β β2)] Γ [(4 + β2) / (4 + β2)]
Above step is rationalizing denominator by multiplying by [(4 + β2) / (4 + β2)]
= [(2 +β5) Γ (4 + β2)] / [(4 β β2) Γ (4 + β2)]
= [(2 +β5) Γ (4 + β2)] / [42 β (β2)2]
= [8 + 2β2 + 4β5 + (β5 Γ β2)] / [16 β (β2 Γ β2)]
= [8 + 2β2 + 4β5 + β(5Γ2)] / [16 β 2]
= [8 + 2β2 + 4β5 + β10] / 14
Square Root Formula
Square root formula is a mathematical expression that calculates the square root of a number. For a non-negative real number xx, the square root y is a number such that y2 = x. A square root is an operation that is used in many formulas and different fields of mathematics.
This article is about square root and square root formulas. The square root of a number is a number squaring which gives the original number. Multiple square root formulas are discussed in this article with their problems.
Table of Content
- Square Root Definition
- Square Root Symbol
- Square Root Formula
- Methods for finding Square Root
- Square Root Table
- Examples on Square Root Formulas