Question

Rationalise 3root2+1 /2root 5-3

Answer 1

Answer:

$\frac{3 \sqrt{2} + 1 }{2 \sqrt{5 } - 3 }$

$\frac{3 \sqrt{2} + 1}{2 \sqrt{5} - 3} \times \frac{2 \sqrt{5} + 3 }{2 \sqrt{5} + 3}$

$\frac{(3 \sqrt{2} + 1)(2 \sqrt{5} + 3) }{ {2 \sqrt{5} }^{2} - {3}^{2} }$

$\frac{(3 \sqrt{2})(2 \sqrt{5}) + (3 \sqrt{2} )(3) + (1)(2 \sqrt{5} ) + (1)(3)}{4(5) - 9}$

$\frac{6 \sqrt{10} + 9 \sqrt{2} + 2 \sqrt{5} + 3}{20 - 9}$

$\frac{6 \sqrt{10} + 9 \sqrt{2} + 2 \sqrt{5} + 3}{11}$

Answer 2

Answer:

\frac{3 \sqrt{2} + 1 }{2 \sqrt{5 } - 3 }

2

5

−3

3

2

+1

\frac{3 \sqrt{2} + 1}{2 \sqrt{5} - 3} \times \frac{2 \sqrt{5} + 3 }{2 \sqrt{5} + 3}

2

5

−3

3

2

+1

×

2

5

+3

2

5

+3

\frac{(3 \sqrt{2} + 1)(2 \sqrt{5} + 3) }{ {2 \sqrt{5} }^{2} - {3}^{2} }

2

5

2

−3

2

(3

2

+1)(2

5

+3)

\frac{(3 \sqrt{2})(2 \sqrt{5}) + (3 \sqrt{2} )(3) + (1)(2 \sqrt{5} ) + (1)(3)}{4(5) - 9}

4(5)−9

(3

2

)(2

5

)+(3

2

)(3)+(1)(2

5

)+(1)(3)

\frac{6 \sqrt{10} + 9 \sqrt{2} + 2 \sqrt{5} + 3}{20 - 9}

20−9

6

10

+9

2

+2

5

+3

\frac{6 \sqrt{10} + 9 \sqrt{2} + 2 \sqrt{5} + 3}{11}

11

6

10

+9

2

+2

5

+3