Square Root of 55
55 is the tenth Fibonacci number. It is an odd composite number. The square root of 55 can be written as 55 raised to the power half. In this mini lesson, let us learn about the square root of 55, find out whether the square root of 55 is rational or irrational, and see how to find the square root of 55 by long division method.
 Square Root of 55: √55 = 7.416
 Square of 55: 55^{2} = 3025
1.  What Is the Square Root of 55? 
2.  Is Square Root of 55 Rational or Irrational? 
3.  How to Find the Square Root of 55? 
4.  FAQs on Square Root of 55 
What Is the Square Root of 55?
 The square root of 55 can be written as √55 in its simplest radical form and (55)^{½ }in the exponential form.
 It means that there is a number a such that: a × a = 55. Now it can also be written as: a^{2} = 55 ⇒a = √55.
 a is the 2nd root of 55 and a = +/7.416
Is Square Root of 55 Rational or Irrational?
The square root of 55 is an irrational number where the numbers after the decimal point go up to infinity. √55 = 7.4161984871. √55 cannot be written in the form of p/q, hence it is an irrational number.
How to Find the Square Root of 55?
The square root of 55 or any number can be calculated in many ways. Two of them are the average method and the long division method.
Square Root of 55 by Average Method
 Take two perfect square numbers, one of which is just smaller than 55 and the other just greater than 55. √49 < √55 < √64
 7 < √ 55 < 8
 Divide 55 by 8 or 7
 Let us divide by 8 ⇒ 55 ÷ 8 = 6. 87
 Find the average of 6.87 and 8
 (6.87+8)/2 = 14.87 ÷ 2 = 7.435
 √55 ≈ 7.4
Square Root of 55 by the Long Division Method
The long division method helps us find the more accurate value of square root of any number. Let's see how to find the square root of 55 by the long division method.
 Step 1: Express 55 as 55.000000. We take the number in pairs from the right. Take 55 as the dividend.
 Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 55.
 Step 3: Now double the quotient obtained in step 2. Here is 2 × 7 = 14. 140 becomes the new divisor.
 Step 4: Apply decimal after quotient '7' and bring down two zeros. We have 600 as the dividend now.
 Step 5: We need to choose a number that while adding to 140 and multiplying the sum with the same number we get a number less than 600. 140+ 4 =144 and 164× 4 = 576. Subtract 576 from 600. We get 24.
 Step 6: Bring down the next pair of zeros. 2400 is the new dividend. Double the quotient. Here it is 148. Have it as 1480. Now find a number at the unit's place of 1480 multiplied by itself gives 2400 or less. We find that 1481 × 1 = 1481. Find the remainder.
 Step 6: Repeat the process until we get the remainder equal to zero. The square root of 55 up to two places is obtained by the long division method. Thus √55 = 7.416
Explore square roots using illustrations and interactive examples.
Tips and Tricks
The square root of any number can be assumed to be between the square root of the two nearest perfect squares of that number. For example, the square root of 55 lies between the square root of 49 and 64. √49 < √56 < √64, i.e., 7 < √55 < 8. Use the average method then, to find the approximate value.
Important Notes
 The square root of 55 is √55 in the radical form, 55^{½} in the exponential form, and 7.416 in the decimal form.
 √55 is an irrational number.
Square Root of 55 Solved Examples

Example 1: Evaluate:
a) √55 + 5√55
b) 2√55 × 5√55
Solution:
a) √55 + 5√55 = √55(1 + 5) = 6√55
b) 2√55 × 5√55 = 2 × √55 × 5 × √55 = 2 × × 5 × √55 × √55 = 10 × 55 = 550

Example 2: Ricky folds a square paper along the diagonal, and the diagonal measures √55. Whal will be the measure of the sides of the paper to the nearest tenth?
Solution: The diagonal of a square is the line joining the opposite vertices of the square.
This diagonal forms the hypotenuse of the square as the right triangle is formed on folding.
side × side = diagonal
side ^{2} = diagonal
side =^{ }√55
side = 7.416
side ≈ 7.4 inch
FAQs on Square Root of 55
What is the square root of 55?
The square root of 55 is approximately equal to 7.416.
How do you write square root of 55 in its simplified form?
√55 is the simplest form of square root of 55.
Is the square root of 55 real?
The square root of 55 is real.
Is √55 a rational number?
√55 is an irrational number, because the value of √55 is a nonteminating decimal on evalulation.
How to find the square root of 55?
The accurate value of √55 can be evaluated using the long division method.
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