Simplify the following:
(i) (5 + √7) (2 + √5)
(ii) (5 + √5) (5 – √5)
(iii) (√5 + √2)2
(iv) (√3 – √7)2
(v) (√2 + √3) (√5 + √7)
(vi) (4 + √5) (√3 – √7)
Solution:
(i) (5 + √7) (2 + √5)
Let us simplify the expression,
= 5(2 + √5) + √7(2 + √5)
= 10 + 5√5 + 2√7 + √35
(ii)(5 + √5) (5 – √5)
Let us simplify the expression,
By using the formula,
(a)2 – (b)2 = (a + b) (a – b)
So,
= (5)2 – (√5)2
= 25 – 5
= 20
(iii)(√5 + √2)2
Let us simplify the expression,
By using the formula,
(a + b)2 = a2 + b2 + 2ab
(√5 + √2)2 = (√5)2 + (√2)2 + 2√5√2
= 5 + 2 + 2√10
= 7 + 2√10
(iv)(√3 – √7)2
Let us simplify the expression,
By using the formula,
(a – b)2 = a2 + b2 – 2ab
(√3 – √7)2 = (√3)2 + (√7)2 – 2√3√7
= 3 + 7 – 2√21
= 10 – 2√21
(v)(√2 + √3) (√5 + √7)
Let us simplify the expression,
= √2(√5 + √7) + √3(√5 + √7)
= √2×√5 + √2×√7 + √3×√5 + √3×√7
= √10 + √14 + √15 + √21
(vi)(4 + √5) (√3 – √7)
Let us simplify the expression,
= 4(√3 – √7) + √5(√3 – √7)
= 4√3 – 4√7 + √15 – √35
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: