Square Root of 343
Taking the square root of a number is raising the number to the power half which is the inverse process of squaring the number. Since 343 is a perfect cube, the square root of 343 is a decimal number and not a whole number. In this mini lesson, let us learn about the square root of 343, find out whether the square root of 343 is rational or irrational, and see how to find the square root of 343 by long division method.
 Square Root of 343: √343 = 18.520
 Square of 343: 343^{2} = 117, 649
1.  What Is the Square Root of 343? 
2.  Is Square Root of 343 Rational or Irrational? 
3.  How to Find the Square Root of 343? 
4.  FAQs on Square Root of 343 
5.  Important Notes on Square Root of 343 
What Is the Square Root of 343?
 If a = b^{2}, then √a = b, where a and b are natural numbers. √a is the square root of a and it is expressed in the exponential form as a^{½ }
 √343 = √(a number × a number).
 √343 = (18.520 × 18.520) or ( 18.520 × 18.520) ⇒ √343= ±18.520
Is Square Root of 343 Rational or Irrational?
Irrational numbers are the real numbers that cannot be expressed as the ratio of two integers. √343 = 18.52025917745213 and hence the square root of 343 is an irrational number where the numbers after the decimal point go up to infinity.
How to Find the Square Root of 343?
The square root of 343 or any number can be calculated in many ways. Two of them are the prime factorization method and the long division method.
Square Root of 343 in its Simplest Radical Form
The square root of 343 is expressed in the radical form as √343. This can be simplified using the prime factorization. Let us 343 as a product of its prime factors. 343 = 7 × 7 × 7. √343 = √(7 × 7 × 7) = 7√7
Square Root of 343 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 343 by the long division method.
 Step 1: Write 343.000000. Take the number in pairs from the right. 1 stands alone. Now divide 3 by a number such that (number × number) gives ≤ 3.
 Obtain quotient = 1 and remainder = 1. Double the quotient. We get 2. Have 20 as our new divisor. Bring down 43 for division.
 Step 2: Find a number such that (20 + that number) × that number gives the product ≤ 2 43. We find that 28 × 8 = 2 24.
 Subtract from 2 43 and get 19 as the remainder. Bring down the pair of zeros. 19 00 is our new divisor.
 Step 3:18 is our quotient and on doubling it becomes 36 and 360 is our new divisor. Find a number such that (360 + the number) × number gets 19 00 or less than that. We find 365 × 5 = 18 25.
 Subtract this from 19 00 and get the remainder and bring down the zeros. 75 00 becomes the new dividend.
 Repeat the steps until we approximate the square root to 3 decimal places. √343 = 18.520
Explore Square roots using illustrations and interactive examples:
Important Notes
 The square root of 343 is 18.520 approximated to 3 decimal places.
 The simplified form of 343 in its radical form is 7√7
 √343 is an irrational number.
Challenging Questions
 What will be the least number to be multiplied or divided by 343 to make it a perfect square?
 Find the square root of √343 up to 3 decimal places.
Square Root of 343 Solved Examples

Example 1: Sandy has to buy a table cloth that could cover the rectangular coffee table of length as twice as its width. What is the length of the cloth that she has to purchase if the area of the table is 686 sq inches?
Solution:
Area of the rectangle = length × width sq inches
length = 2 × width inches
Area of the rectangle = 2 × width × width = 686 sq inches
2 width^{2 }= 686 sq inches
width^{2} = 686 ÷ 2 = 343 inches
Width = √343 = 18.52
Length = 2 × width
= 2 × 18.52 = 37.04
Length of the coffee table = 37.04 inches
She needs to buy a few inches longer than her coffee table, preferably 40 inches long cloth. 
Example 2: Evaluate: √343 × √175
Solution:
√343 = √(7 × 7 ×7) = 7√7
√175 = √(5 × 5 × 7) = 5√7
=√343 × √175 = 7√7 × 5√7
=√7 × √7 × 5 × 7 = 7 × 35 = 245
=√343 × √175 = 245
FAQs On Square Root of 343
What is the square root of 343?
The square root of 343 is √343 = 18.520
What is the square root of 343 simplified?
7√7 is the simplest form of √343
How to get the square root of 343?
The square root of 343 is evaluated by the long division method.
Is √343 a rational number?
√343 is an irrational number, because the value of √343 is not a whole number and it is a nonterminating decimal.
How to find the square root of 343 to the nearest hundredth?
The square root of 343 is evaluated using the division method and rounded off to the nearest hundredth.√343 = 18.520 ⇒ √343 = 18.52
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