Question

simplify:7√3/√10+√3-2√5/√6+√5-3√2/√15+3√2​

Answer 1

Solution :-

First part of Question is :-

(7√3)/(√10 + √3)

second Part :-

(2√5)/(√6 + √5)

Third Part :-

(3√2)/(√15 + 3√2)

Solving Each part one by one Now :-

1) (7√3)/(√10 + √3)

→ (7√3)/(√10 + √3)

Rationalising the denominator we get,

→ {(7√3)/(√10 + √3)} * {(√10 - √3) / (√10 - √3)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {7√3*(√10 - √3)} / (10 - 3)

→ {7√3*(√10 - √3)} / 7

→ √3(√10 - √3)

→ (√30 - 3)

2) (2√5)/(√6 + √5)

→ (2√5)/(√6 + √5)

Rationalising the denominator we get,

→ {(2√5)/(√6 + √5)} * {(√6 - √5) / (√6 - √5)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {2√5 * (√6 - √5)} / (6 - 5)

→ 2√5 * (√6 - √5)

→ 2√30 - 2*5

→ (2√30 - 10).

3) (3√2)/(√15 + 3√2)

→ (3√2)/(√15 + 3√2)

Rationalising the denominator we get,

→ {(3√2)/(√15 + 3√2)} * {(√15 - 3√2) / (√15 - 3√2)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {3√2 * (√15 - 3√2)} / (15 - 18)

→ {3√2 * (√15 - 3√2)} / (-3)

→ (-1) * √2 * (√15 - 3√2)

→ - √30 + 3*2

→ (6 - √30).

Therefore,

→ (7√3)/(√10 + √3) - (2√5)/(√6 + √5) - (3√2)/(√15 + 3√2)

→ (√30 - 3) - (2√30 - 10) - (6 - √30)

→ √30 - 2√30 + √30 - 3 + 10 - 6

→ 2√30 - 2√30 + 10 - 9

→ 10 - 9

→ 1. (Ans.)

Hence , Required Answer is 1.

Answer 2

Answer:

Solution :-

First part of Question is :-

(7√3)/(√10 + √3)

second Part :-

(2√5)/(√6 + √5)

Third Part :-

(3√2)/(√15 + 3√2)

Solving Each part one by one Now :-

1) (7√3)/(√10 + √3)

→ (7√3)/(√10 + √3)

Rationalising the denominator we get,

→ {(7√3)/(√10 + √3)} * {(√10 - √3) / (√10 - √3)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {7√3*(√10 - √3)} / (10 - 3)

→ {7√3*(√10 - √3)} / 7

→ √3(√10 - √3)

→ (√30 - 3)

2) (2√5)/(√6 + √5)

→ (2√5)/(√6 + √5)

Rationalising the denominator we get,

→ {(2√5)/(√6 + √5)} * {(√6 - √5) / (√6 - √5)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {2√5 * (√6 - √5)} / (6 - 5)

→ 2√5 * (√6 - √5)

→ 2√30 - 2*5

→ (2√30 - 10).

3) (3√2)/(√15 + 3√2)

→ (3√2)/(√15 + 3√2)

Rationalising the denominator we get,

→ {(3√2)/(√15 + 3√2)} * {(√15 - 3√2) / (√15 - 3√2)}

using (a + b)(a - b) = a² - b² in Denominator now,

→ {3√2 * (√15 - 3√2)} / (15 - 18)

→ {3√2 * (√15 - 3√2)} / (-3)

→ (-1) * √2 * (√15 - 3√2)

→ - √30 + 3*2

→ (6 - √30).

Therefore,

→ (7√3)/(√10 + √3) - (2√5)/(√6 + √5) - (3√2)/(√15 + 3√2)

→ (√30 - 3) - (2√30 - 10) - (6 - √30)

→ √30 - 2√30 + √30 - 3 + 10 - 6

→ 2√30 - 2√30 + 10 - 9

→ 10 - 9

→ 1. (Ans.)

Hence , Required Answer is 1.