Question

find cube root of 458​

Answer 1

Finding Cubeth Root of a number :

Given number : 458

To find : Cubeth Root of 458

Solution :

Firstly, we need to determine if the given number is perfect cube or not. Is it? NO! 458 is not a perfect cube.

If the number is a perfect cube, you can go by prime factrization. As it is not, here we bring some awesome and easy method to you to find the cube of given non perfect cube number 458.

Step 1 :

Take the neighbouring perfect cubes of given number 458, which are 343 (7³) and 512 (8³)

So, the cube root of 458 lies in between 7 and 8. As 458 is more nearer to 512, the value will be greater than 7.5

So, we know that the INTEGRAL PART of CUBE ROOT of 458 is 7. Now, we need to find the DECIMAL part.

Step 2 :

Now, let us try to get more precise value. So, take the least nearer perfect cube, which is 343.

Divide 343 with its cube root value's square i.e.,

343 / 7²  = 343 / 49 = 9.3469

Step 3 :

Subtract the cube root value 7 from the leaded value 9.3469.

9.3469 - 7 = 2.3469

Step 4 :

Now, divide 2.3469 value with half of 7 which is 3.5

2.3469 / 3.5 = 0.67

Now 0.67 is the DECIMAL PART of CUBE ROOT of 458.

Step 5 :

Add both integral and decimal parts.

7+0.67 = 7.67 = 7.7 (approximately)

7.7 is the cube root of 458.

Through this method, we will get the approximate values. The actual root of 458 is 7.7082 which is rounded to 7.7

Learn more :

1. Shortcut to find cube root of non perfect cube root

https://brainly.in/question/3534874

2. Simplify 2 cube root + 16 cube root - 54 cube root​

https://brainly.in/question/12051972