Question

simplify each of the following by rationalising the denominator of 1/5+√2​

Answer 1

Step-by-step explanation:

ANSWER

1)

6+4

2

6−4

2

=

6+4

2

6−4

2

×

6−4

2

6−4

2

=

(6)

2

−(4

2

)

2

(6−4

2

)

2

=

4

36+32−48

2

=17−12

2

2)

7

+

5

7

−

5

=

7

+

5

7

−

5

×

7

−

5

7

−

5

=

(

7

)

2

−(

5

)

2

(

7

−

5

)

2

=

2

7+5−2

35

=6−

15

3)

3

2

−2

3

1

=

3

2

−2

3

1

×

3

2

+2

3

3

2

+2

3

=

(3

2

)

2

−(2

3

)

2

3

2

+2

3

=

6

3

2

+2

3

Answer 2

Answer:

$\frac{1}{5 + \sqrt{2} } \\ \\ = \frac{1}{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} } \\ \\ = \frac{5 - \sqrt{2} }{ {(5)}^{2} - {( \sqrt{2} )}^{2} } \\ \\ = \frac{5 - \sqrt{2} }{25 - 2} \\ \\ = \frac{5 - \sqrt{2} }{23}$

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