If √2 = 1.414, then find the value of
(i) √8 + √50 + √72 + √98
(ii) 3√32 – 2√50 + 4√128 – 20√18
Solution:
(i) √8 + √50 + √72 + √98
Let us simplify the expression,
√8 + √50 + √72 + √98
= √(2×4) + √(2×25) + √(2×36) + √(2×49)
= √2 √4 + √2 √25 + √2 √36 + √2 √49
= 2√2 + 5√2 + 6√2 + 7√2
= 20√2
= 20 × 1.414
= 28.28
(ii) 3√32 – 2√50 + 4√128 – 20√18
Let us simplify the expression,
3√32 – 2√50 + 4√128 – 20√18
= 3√(16×2) – 2√(25×2) + 4√(64×2) – 20√(9×2)
= 3√16 √2 – 2√25 √2 + 4√64 √2 – 20√9 √2
= 3.4√2 – 2.5√2 + 4.8√2 – 20.3√2
= 12√2 – 10√2 + 32√2 – 60√2
= (12 – 10 + 32 – 60) √2
= -26√2
= -26 × 1.414
= -36.764
More Solutions:
- Find the greatest and the smallest real numbers.
- Write in ascending order.
- Write in descending order.
- Arrange in ascending order.
- Rationalize the denominator of the following:
- Simplify each of the following by rationalizing the denominator:
- Simplify the rational and irrational numbers:
- Simplify the following rational numbers:
- Give a and b are rational numbers. Find a and b if: