Taking the square source of a number is raising the number to the power half which is the inverse procedure 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 united state learn around the square root of 343, discover out whether the square source of 343 is rational or irrational, and see how to find the square source of 343 by long department method. 

Square root of 343343 = 18.520Square that 343: 3432 = 117, 649
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What Is the Square source of 343?
2.Is Square root of 343 rational or Irrational?
3.How to find the Square source of 343?
4.FAQs on Square root of 343
5.Important note on Square root of 343

What Is the Square source 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 2 integers. √343 = 18.52025917745213 and also hence the square source of 343 is one irrational number wherein the number after the decimal point go approximately infinity.


How to discover the Square root of 343?


The square source of 343 or any kind of number deserve to be calculation in countless ways. 2 of them are the prime administer method and the long division method.

Square root of 343 in its easiest Radical Form

The square root of 343 is expressed in the radical kind as √343. This have the right to be streamlined using the prime factorization. Permit us 343 together a product of its prime factors. 343 = 7 × 7 × 7. √343 = √(7 × 7 × 7) = 7√7

Square source of 343 by the Long division Method

The long division method helps us to discover a an ext accurate worth of square root of any number. The complying with are the steps to advice the square source of 343 by the long division method.

Step 1: compose 343.000000. Take the number in pairs from the right. 1 was standing alone. Now division 3 through a number such that (number × number) offers ≤ 3.Obtain quotient = 1 and also remainder = 1. Double the quotient. We acquire 2. Have actually 20 as our new divisor. Bring under 43 for division.Step 2: Find a number such that (20 + that number) × that number offers the product ≤ 2 43. We uncover that 28 × 8 = 2 24.Subtract native 2 43 and get 19 together the remainder. Carry down the pair that zeros. 19 00 is our new divisor.Step 3:18 is our quotient and on doubling it becomes 36 and also 360 is our new divisor. Find a number such the (360 + the number) × number it s okay 19 00 or much less than that. We find 365 × 5 = 18 25. Subtract this native 19 00 and also get the remainder and bring under the zeros. 75 00 becomes the new dividend.Repeat the procedures until us approximate the square root to 3 decimal places. √343 = 18.520

 

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Important Notes


The square root of 343 is 18.520 approximated to 3 decimal places.The simplified kind of 343 in its radical form is 7√7√343 is one irrational number.

Challenging Questions


What will be the least number to be multiplied or split by 343 to do it a perfect square?Find the square source of √343 as much as 3 decimal places.

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Example 1: Sandy has to buy a table fabric that could cover the rectangular coffee table of length as twice as that width. What is the length of the towel that she has to purchase if the area the the table is 686 sq inches?

Solution:

Area of the rectangle = length × broad sq incheslength = 2 × width inchesArea the 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 the the coffee table = 37.04 inchesShe needs to purchase 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