
Find the cube root of the number – 17576 using the factorization method.
Answer
450.7k+ views
Hint: To find the cube root of the number we factorize the given number until we get a number which is raised to the power of 3.
Complete step-by-step answer:
Let us first find the cube root of 17576, i.e.
We express the number 17576 as a product of prime numbers.
We have,
17576 =2 × (8788)
=2 × 2 × (4394)
=2 × 2 × 2 × (2197)
=2 × 2 × 2 × 13 × (169)
=2 × 2 × 2 × 13 × 13 × 13
= (2 × 13) × (2 × 13) × (2 × 13)
= 26 × 26 × 26.
This shows that −17567 = (−26) × (−26) × (−26).
Thus −17576 = .
The cube root of – 17567, i.e. - = -26.
Note: In order to solve such types of problems the key is to express the given number as a product of prime numbers, then we rewrite all its factors until we achieve a number raised to the power 3 as we are supposed to find the cube root.
We apply the same procedure to find the square root, fourth root, fifth root and so on of a number, we write down all the factors of the number and try to express them as a number raised to the power of 4 for fourth root, power 5 for the fifth root and so on.
Complete step-by-step answer:
Let us first find the cube root of 17576, i.e.
We express the number 17576 as a product of prime numbers.
We have,
17576 =2 × (8788)
=2 × 2 × (4394)
=2 × 2 × 2 × (2197)
=2 × 2 × 2 × 13 × (169)
=2 × 2 × 2 × 13 × 13 × 13
= (2 × 13) × (2 × 13) × (2 × 13)
= 26 × 26 × 26.
This shows that −17567 = (−26) × (−26) × (−26).
Thus −17576 =
The cube root of – 17567, i.e. -
Note: In order to solve such types of problems the key is to express the given number as a product of prime numbers, then we rewrite all its factors until we achieve a number raised to the power 3 as we are supposed to find the cube root.
We apply the same procedure to find the square root, fourth root, fifth root and so on of a number, we write down all the factors of the number and try to express them as a number raised to the power of 4 for fourth root, power 5 for the fifth root and so on.
Latest Vedantu courses for you
Grade 6 | CBSE | SCHOOL | English
Vedantu 6 Pro Course (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Chemistry: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Trending doubts
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How many ounces are in 500 mL class 8 maths CBSE

How many ten lakhs are in one crore-class-8-maths-CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE

One cusec is equal to how many liters class 8 maths CBSE
