Square Root of 161

The square root of 161 is expressed as √161 in the radical form and as (161)^½ or (161)^0.5 in the exponent form. The square root of 161 rounded up to 6 decimal places is 12.688578. It is the positive solution of the equation x² = 161.

• Square Root of 161: 12.68857754044952
• Square Root of 161 in exponential form: (161)^½ or (161)^0.5
• Square Root of 161 in radical form: √161

The square root of a number n is written as √n. This number when squared or multiplied by itself gives the original number n. The square root of 161 can be represented in multiple ways:

• Radical form: √161 
• Decimal form: 12.688
• Exponent form: (161)^1/2

There are 2 ways to find the square root of 161:

• Long Division Method
• Prime Factorization

One can find out other methods by clicking here.

Long Division Method

The square root of 161 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits of 161 by putting a bar above 61 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
• Step 2: Find a number which, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisor's place, which will result in the remainder being 0. 
• Step 3: Drag down 61 beside the remainder 0. Also, add the divisor to itself and write it below. (1 + 1 = 2).
• Step 4:  Find a number X such that 2X × X results in a number less than or equal to 61. The number 2 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient. 
• Step 5: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor becomes 24. 
• Step 6: Repeat this process to get the decimal places you want.

Therefore, the square root of 161 = 12.688.

Estimation and Approximation

The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.

• First, we will find the two consecutive numbers such that 161 lies between their perfect squares. In this case, the numbers are 12 (144) and 13 (169). We take the whole number part to be the smaller perfect square, in this case, 12.
• Now, for the decimal part we will use the below formula: (Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
  = (161 - 144)/(169 - 144) = 17/25 = 0.68

Therefore, the square root of 161 ≅ 12.68.

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