Page 39 - SM inner class 8.cdr

Summary

m If a number is multiplied two times by itself is called cubed number.
m A cube is equal to a number raised to power 3.
m In order to check whether a number is a perfect cube or not, we find its prime factors and group together
triplets of the same prime factors.
m We can estimate cube root by following the table and some simple steps mentioned in this chapter.
m There are some patterns which involve cubic numbers as:
3
3
2 - 1 = + ´ ´1 2 1 3
3
3
3 - 2 = + ´ ´1 3 2 3
3
3
3
4 - 3 = +1 4 ´ ´3
3
3
5 - 4 = + ´ ´3
4
5
1
3
3
1
6
5
6 - 5 = + ´ ´3 and so on.
Review Exercise
1. Find the cubes of the following numbers:
(i) 8 (ii) 16 (iii) 21 (iv) 30
2. Test whether the given numbers are perfect cubes or not.
(i) 243 (ii) 516 (iii) 729 (iv) 8000
(v) 27000
3. Find the small est number by which 8788 must be multi plied to obtain a perfect cube?
4. What small est number should 7803 be multi plied with so that the prod uct becomes a perfect cube?
5. Find the small est number by which 8640 must be divided so that the quotient is a perfect cube?

6. Find the cube root of the following numbers by prime factorization method.
(i) 343 (ii) 729 (iii) 1.331 (iv) 2744/8000
7. Find the cube root of the follow ing numbers through esti ma tion?
(i) 512 (ii) 2197 (iii) 3375 (iv) 5832

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Mathematics In Focus - 8