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# !Surd manipulation! watch

1. Hi!

I am totataly confused with rationalising the denominator and multiplying surds. For example:

1+√2 x √2

and...

3√2
√8

also... how would you rationalise this denominator:

1+√2
√2

Arggh Im sooo confused
2. root 2 times root 2 is simply 2.
3. You can simplify the root 8 to 2 root 2.
4. Or simply change the denominator into

which then simply becomes

5. (Original post by TomLeigh)
Or simply change the denominator into

which then simply becomes

How does it become 3/2
6. When you have the same thing as the numerator and the denominator you can just cancel them out, as it is the same as multiplying

which is ultimately the same as
7. (Original post by TomLeigh)
When you have the same thing as the numerator and the denominator you can just cancel them out, as it is the same as multiplying

which is ultimately the same as
how does 1+√2 x √2 =3
???
8. root 2 * root 2
= root 4
9. Well if you multiply two of the same surds together then you just get the number within the surd. This can also be explained using indices:

As when multiply similar numbers with indices, you add the indices.
10. (Original post by TomLeigh)
When you have the same thing as the numerator and the denominator you can just cancel them out, as it is the same as multiplying

which is ultimately the same as

To be honest, if someone is having problems with surds, that's probably just going to add confusion.
11. (Original post by Sophie Maywood)
Hi!

I am totataly confused with rationalising the denominator and multiplying surds. For example:

1+√2 x √2

and...

3√2
√8

also... how would you rationalise this denominator:

1+√2
√2

Arggh Im sooo confused
1 + √2 x √2
√2 x √2 = √4
√4 = 2
1 + 2 = 3

3√2
√8
√8 = √4 x √2 (look for the largest square number - 4)
√4 = 2
3√2
2√2
3 (multiply the numerator and denominator by √2)
2

1+√2
√2
3 (multiply top and bottom by √2)
2
12. (Original post by TomLeigh)
Well if you multiply two of the same surds together then you just get the number within the surd. This can also be explained using indices:

As when multiply similar numbers with indices, you add the indices.
that is just confusing for someone who's not good with surds... all you need to know is that:

(Original post by Sophie Maywood)
how does 1+√2 x √2 =3
???
using what i just wrote above

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