Describe the method of finding Square root of a number using long divison method.
2.using the the above method find the square root of:
a.119.57
b.98.01. Express both answer correct up to 2 decimel places.
Answers
Answer:
The square root of 2 is expressed as √2 in the radical form and as (2)½ or (2)0.5 in the exponent form. The square root of 2 rounded up to 10 decimal places is 1.4142135624. It is the positive solution of the equation x2 = 2.
Square Root of 2: 1.4142135623730951
Square Root of 2 in exponential form: (2)½ or (2)0.5
Square Root of 2 in radical form: √2
What Is the Square Root of 2?
Square root is just an inverse operation of square. The square root of 2 is represented as √2. This is a number which when multiplied to itself gives us the result as 2. During ancient times, Greeks found a number that can never ever be written in the form of p/q, where p,q are integers and q is not equal to 0. This means √2 is not rational. √2 happens to be very useful in geometry. Let's say we have a square with side length 1 and you want to find the length of the diagonal.
Finding Square Root of 2
To find the third side we use Pythagoras Theorem. The third side will be √2. Let's locate the number √2 on a number line. We will use transfer the square we used to discover √2. Let's name the vertices of the square as shown. Keep the vertex O at 0. We already discovered that OB=√2
Using a compass with centre O and radius OB, draw an arc intersecting the number line at the point P.
Square Root 2 on a Number Line.
The point P corresponds to √2 on the number line.
Is the Square Root of 2 Rational or Irrational?
The actual value of √2. is undetermined. The value of √2 upto 25 decimal places is 1.4142135623730950488016887..
At present, the value of √2 is known up to 1 trillion decimal place.
Hence, √2 is irrational.
Important Notes:
√2 is also called Pythagoras' constant.
√2 represents the diagonal of a unit square.
√2 was the first number to be discovered as an irrational number.
Its decimal representation is non-terminating and non-repeating.
The ratio of longer edge and shorter edge of an A4 size sheet paper is equal to √2.
How to Find the Square Root of 2?
We can find the square root of 2 by the following two methods:
Long Division Method
Estimation and Approximation Method
Square Root of 2 by Long Division Method
The value of square root of 2 by long division method consists of following steps:
Step 1: Find the largest number whose square is less than or equal to the number 2. Take this number as the divisor and the quotient, (1 in this case). Divide and write the remainder.
Step 2: In the quotient, put a decimal point after 1. Bring down two zeroes to the right of the remainder. So, the new dividend is 100
Step 3: Double the divisor and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder. Repeat this process to get the decimal places you want.
Square Root of 2 by Long Division
Please mark me as brainliest.
please