To find the square root of 29, we can use any method – prime factorisation, Newton’s formula for square, long division method, etc. As 29 is not a perfect square number, we get an irrational root. A perfect square number is a number that can be written as a square of an integer and whose square is a whole number. The square root of a number is just the opposite of squaring. In radical form, the square root of 29 is denoted as √29, and in the exponential form, it is written as (29)½. Let us learn how to find the square root of 29.
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Square Root of 29 |
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Square of 29 |
841 |
What Is the Square Root of 29?
The square root of 29 is a number whose square gives the result of 29. Now, 29 is not a perfect square number because we cannot find any integer which could be multiplied twice to get 29. Thus, we find an approximate value of the square root of 29, as it is an irrational number.
The square root of 29 can also be determined by finding the roots of the quadratic equation
x2 – 29 = 0
⇒ x2 = 29
Taking square roots on both sides, we get,
⇒ x = √29
⇒ x = ± 5.385 (approximately)
How to Find the Square Root of 29?
Let us find the square root of 29 using Newton’s square root equation, prime factorisation, and the long division method. The repeated subtraction method will not work, as 29 is not a perfect square, and its square root is an irrational number. Still, we shall see what result we get when trying to find the square root of 29 using the repeated subtraction method.
Repeated Subtraction Method
The square root of any perfect square number can be determined by repeatedly subtracting consecutive odd positive integers from the given number until the answer is zero. The value of n for which the nth step results in zero is the square root of the given number.
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Step 1 |
29 |
– |
1 |
= |
28 |
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Step 2 |
28 |
– |
3 |
= |
25 |
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Step 3 |
25 |
– |
5 |
= |
20 |
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Step 4 |
20 |
– |
7 |
= |
13 |
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Step 5 |
13 |
– |
9 |
= |
4 |
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Step 6 |
4 |
– |
11 |
= |
-7 |
After the 5th step, instead of getting zero as the answer, we get a negative integer. Thus, this method cannot simplify the square root of 29. We get an estimation that the square root of 29 lies between 5 and 6, which is an irrational number.
Newton’s Square Root Equation
Newton’s square root equation to find the square root of any number is given by
Where
N is the number whose square root we need to find.
X is the approximate guess square root number.
Now, we have N = 29, as 52 = 25 < 29, we take X = 8. Let us put all the values in the given formula to find the square root of 29.
√29 ≈ ½ (29/5 + 5) = ½ (5.8 + 5)
= 10.8/2 = 5.4, which is quite close to the actual square root of 29.
Prime Factorisation Method
To find the square root of 29 by the prime factorisation method, we first prime factorise 29 and then make pairs of two to get the square root. Since 29 is a prime number,
the prime factorisation of 29 = 29 (as 29 is a prime number)
The square root of 29 = √29 ≈ 5.385 (approx.)
Clearly, we cannot make any pair of factors of 29. Thus, the square root of 29 cannot be simplified using the prime factorisation method.
Long Division Method
To find the square root of 29 by the long division method, we shall write 29 as the dividend and pair its digits from right to left. Now, we shall calculate the square root:
To learn how to find the square root of any number by the long division method, click here.
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Solved Examples on Square Root of 29
Example 1:
Find the semi-perimeter of the circle whose area is 29𝜋 m2.
Solution:
Let r be the radius of the circle.
The area of the circle = 𝜋r2 = 29𝜋 m2
⇒ r2 = 29 (taking square root on both sides)
⇒ r = √29
⇒ r ≈ 5.385 m (taking the positive root as length cannot be negative)
∴ the semi-perimeter of the circle = 2𝜋r ÷ 2 = 𝜋r = 𝜋 × 5.385 = 3.14 × 5.385 = 16.91 m (approx.)
Example 2:
Find the length of the base of a triangle whose area is 2.9 m2 and the height is one-fifth of its base.
Solution:
Let ‘b’ be the base of the triangle.
Height of the triangle = b/5
Area of the triangle = ½ × b × b/5 = 2.9 m2
⇒ 1/10 × b2 = 2.9
⇒ b2 = 2.9 × 10 = 29 (taking square root on both the sides)
⇒ b = √29 ≈ 5.385 m
∴ the length of the base of the triangle is 5.385 m.
Example 3:
What is the smallest number that should be subtracted from 29 to make it a perfect square number? Also, find the square root of that number obtained.
Solution:
Clearly, 52 = 25 < 29 is the greatest perfect square number less than 29.
Therefore, we must subtract 4 from 29 to make it a perfect square number.
29 – 4 = 25
And √25 = ± 5
Frequently Asked Questions on Square Root of 29
What is the square root of 29?
The square root of 29 is 5.385164807 (approx.).
Is 29 a perfect square number?
No, 29 is not a perfect square number, as it cannot be expressed as the square of any integer.
Is the square root of 29 rational or irrational?
The square root of 29 is an irrational number.
What is the prime factorisation of 29?
The prime factorisation of 29 is 29 as it is a prime number.
Is the square root of 29 a real number?
Yes, the square root of 29 is a real number.
What is the cube root of 29?
The cube root of 29 is 3.0723168 (approx.).
What number should be subtracted from 29 to get a perfect square number?
As 52 = 25 < 29, 4 must be subtracted from 29 to get a perfect square number.
