Square Root of 119

The square root of 119 is expressed as √119 in the radical form and as (119)^½ or (119)^0.5 in the exponent form. The square root of 119 rounded up to 8 decimal places is 10.90871211. It is the positive solution of the equation x² = 119.

• Square Root of 119: 10.908712114635714
• Square Root of 119 in exponential form: (119)^½ or (119)^0.5
• Square Root of 119 in radical form: √119

• The square root of 119 ⇒ √119 =  √(a × a). Thus a = √119
• . √119 = √(10.908 × 10.908) or √(-10.908 × -10.908) ⇒ √119 = ±10.908
• We know that on prime factorization, 119 = 7 × 17. Thus  √119  cannot be expressed in the simplest radical form. The radical form of  √119 is  √119.

Irrational numbers are the real numbers that cannot be expressed as the ratio of two integers.  √119 = 10.90871211463571 and hence the square root of 119 is an irrational number where the numbers after the decimal point go up to infinity.

The square root of 119 or any number can be calculated in many ways. Two of them are the approximation method and the long division method.

Square Root of 119 by Approximation Method

• Take two perfect square numbers, one of which is just smaller than 119 and another one just greater than 119. √100 < √119 < √121
• 10 <  √ 119 < 11
• Using the average method, divide 119 by 10 or 11.
• Let us divide by 11 ⇒ 119 ÷ 11 = 10.818
• Find the average of 10.818 and 11.
• (10.818 + 11) / 2 = 21.818 ÷ 2 = 10.909
• √119 ≈  10.909

Square Root of 119 by the Long Division Method

The long division method helps us to find a more accurate value of square root of any number. The following are the steps to evaluate the square root of 119 by the long division method.

• Step 1: Write 119.000000. Take the number in pairs from the right. 1 stands alone. Now divide 1 by a number such that (number × number) gives  ≤ 1.
• Obtain quotient = 1 and remainder = 0. Double the quotient. We get 2. Have 20 as our new divisor. 
• Step 2: Find a number such that (20 + that number) × that number gives the product ≤ 16.  We cannot find a number that divides 16. Bring down two zeros. 19 00 is our new dividend.
• 10 is our quotient and on doubling, it becomes 20 and 200 is our new divisor. Find a number such that (200 + the number) × number gets 19 00 or less than that. We find 9 is such number. 209 × 9 = 18 81
• Step 3: Quotient is 10.9 and the remainder is 19. Bring down the next pair of zeros and 19 00 becomes the new dividend. 
• Double the quotient. 109 × 2 = 218. Have 2180  in the place of the new divisor. Find a number such that (2180 + that number) × number ≤ 19 00. 
• We cannot find a number that divides 19 00. Bring down two zeros. 19 00 00 is our new dividend.
• Quotient is 10.90 . Doubling it we get 2180.
• Repeat the steps until we approximate the square root to 3 decimal places. √119 =  10.908

Explore square roots using illustrations and interactive examples

• Square root of 117
• Square root of 123
• Square root of 135
• Square root of 180
• Square root of 120

• The square root of 119 lies between the square root of 100 and 121.  Therefore, 10 < √119 < 11. It is closer to the perfect square 121.
• 19 is the least number to be subtracted and 2 is the least number to be added to make it a perfect square. (119 - 19 = 100) and (119 + 2 = 121)

• Find the square root of 119 up to 7 decimal places.
• Find the square root of √119.