Square root of a number is the factor that we multiply by itself two times to get that number. Consider the following
Here 36 is a perfect square, because we can write 36 as square of 6.
To find a square root of a number, we will follow the steps.
Step 1 :
Decompose the numerator and denominator separately as product of prime factors.
Step 2 :
For every two same values, we can take one out of the square root.
Finding square root of rational number ?
Using the following property, we find square root of rational number.
Evaluate each of the following.
Problem 1 :
√1/25
Solution :
= √1/25
= √1/√25
= √(1 ⋅ 1) / √(5 ⋅ 5)
= 1/5
Problem 2 :
√1/81
Solution :
= √1/81
= √1/√81
= √(1 ⋅ 1)/√(9 ⋅ 9)
= 1/9
Problem 3 :
-√36/144
Solution :
= -√36/144
= -√36/√144
= -√(6 ⋅ 6)/√(12 ⋅ 12)
= -6/12
= -1/2
Problem 4 :
√529/625
Solution :
= √529/625
= √529/√625
= √(23 ⋅ 23)/√(25 ⋅ 25)
= 23/25
Problem 5 :
√16/25
Solution :
= √16/25
= √16/√25
= √(4 ⋅ 4)/√(5 ⋅ 5)
= 4/5
Determine whether each of the following statements in true or false.
Problem 1 :
-√36/324 = 1/3
Solution :
= -√36/324
= -√36/√324
= -√(6⋅6)/√(18⋅18)
= -6/18
= -1/3
So, the statement is false.
Problem 2 :
√324/625 = 18/25
Solution :
= √324/625
= √324/√625
= √(18⋅18)/√(25⋅25)
= 18/25
So, the statement is true.
Problem 3 :
-√900/961 = -30/31
Solution :
= -√900/961
= -√900/√961
= -30/31
So, the statement is true.
Problem 4 :
√1/4 = ± 1/2
Solution :
= √1/4
= √1/√4
= ± 1/2
So, the statement is true.
Problem 5 :
If x/y = -2, find √ (x²/y² + y²/x²)
Solution :
√ (x²/y² + y²/x²) = √ (x/y)² + (y/x)²
= √ (x/y)² + (x/y)^{-}²
= √ (-2)^{2} + (-2)^{-2}
= √4 + 1/4
= √17/4
= √17/√4
= √17/2
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM