Taking the square root of a number is raising the number to the power half which is the inverse process of squaring the number. Due to the fact that 343 is a perfect cube, the square root of 343 is a decimal number and not a entirety number. In this mini lesboy, let us learn about the square root of 343, find out whether the square root of 343 is rational or irrational, and also check out just how to find the square root of 343 by long division technique.

**Square Root of 343**:

**√**343 = 18.520

**Square of 343: 343**2 = 117, 649

1. You are watching: Square root of 343 in radical form | 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?

√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 proportion of two integers. √343 = 18.52025917745213 and hence the square root of 343 is an irrational number wright here the numbers after the decimal allude go as much as infinity.

## How to Find the Square Root of 343?

The square root of 343 or any kind of number have the right to be calculated in many kind of ways. Two of them are the prime factorization method and the lengthy department strategy.

### Square Root of 343 in its Simplest Radical Form

The square root of 343 is expressed in the radical create as √343. This deserve to be simplified utilizing the prime factorization. Let us 343 as a product of its prime determinants. 343 = 7 × 7 × 7. √343 = √(7 × 7 × 7) = 7√7

### Square Root of 343 by the Long Division Method

The lengthy department method helps us to uncover a much more accurate worth of square root of any type of number. The complying with are the steps to evaluate the square root of 343 by the long department strategy.

**Step 1**: Write 343.000000. Take the number in pairs from the best. 1 stands alone. Now divide 3 by a number such that (number × number) provides ≤ 3.Obtain quotient = 1 and also remainder = 1. Double the quotient. We acquire 2. Have 20 as our new divisor. Bring down 43 for division.

**Step 2:**Find a number such that (20 + that number) × that number provides the product ≤ 2 43. We discover that 28 × 8 = 2 24.Subtract from 2 43 and also gain 19 as the remainder. Bring dvery own the pair of zeros. 19 00 is our new divisor.

**Step 3:**18 is our quotient and also on doubling it becomes 36 and also 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 also obtain the remainder and bring down the zeros. 75 00 becomes the new dividfinish.Repeat the actions until we approximate the square root to 3 decimal areas.

**√343 = 18.520**

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**Important Notes**

The square root of 343 is 18.520 approximated to 3 decimal areas.The simplified form of 343 in its radical develop is 7√7√343 is an irrational number.

**Challenging Questions**

What will be the leastern number to be multiplied or separated by 343 to make it a perfect square?Find the square root of √343 up to 3 decimal areas.

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**Example 1**: Sandy has to buy a table fabric that could cover the rectangular coffee table of size as twice as its width. What is the size of the cloth that she hregarding purchase if the location of the table is 686 sq inches?

**Solution:**

Area of the rectangle = length × width sq inches**length = 2 × width inchesArea of the rectangle = 2 × width × width = 686 sq inches2 width2 = 686 sq incheswidth2 = 686 ÷ 2 = 343 inchesWidth = √343 = 18.52 Length = 2 × width = 2 × 18.52 = 37.04 Length of the coffee table = 37.04 inchesShe requirements to buy a few inches much longer than her coffee table, preferably 40 inches lengthy 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**