Question

7√3/√10+√3 - 2√5/√6+√5 - 3√2/√5+3√2​

Answer 1

Answer:

The Answer is $\huge\red{\boxed{\tt{1}}}$

Step-by-step explanation:

$\huge\pink{\bold{\tt{Solution :}}}$

First part of Question is :

• (7√3)/(√10+√3)

Second Part :

• (2√5)/(√6 + √5)

Third Part :

• (3√2)/(√15 + 3√2)

.

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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* (v15 - 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 -

→ 2√30 - 2√30 + 10 - 9

→ 10 - 9

→ $\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{\boxed{\tt{</strong><strong>1</strong><strong>}}}$

$\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{\</strong><strong>s</strong><strong>f</strong><strong>\</strong><strong>u</strong><strong>n</strong><strong>d</strong><strong>e</strong><strong>r</strong><strong>l</strong><strong>i</strong><strong>n</strong><strong>e</strong><strong>{\tt{</strong><strong>Hence, Required</strong><strong>\</strong><strong>:</strong><strong>Answer</strong><strong>\</strong><strong>:</strong><strong>is</strong><strong>}}}$ $\</strong><strong>l</strong><strong>a</strong><strong>r</strong><strong>g</strong><strong>e</strong><strong>\green{\boxed{\tt{1}}}$