How do i do this surd question? 3√40+6√90

please help I'm not good at surds

This problem is just like doing fractions. You have to have a common radical like you have to have a common denominator.

3√40+6√90

√(40)
√(2*20)
√(2*5*4)
√(2*5*2*2)
2√10

√(90)
√(30*3)
√(10*3*3)
3√10

Now the problem is 6√10+18√10
The answer is 24√10.

A lot of people are a bit puzzled by surds but actually they aren't that difficult.

Look at the number behind the square root sign and ask yourself what are its factors.
You are only interested in a factor if it is a perfect square (i.e. 4, 9, 16, 25, 36, 49, 64, 81 and so on)

So for example, 40 has factors 4 x 10 so √40 can be written as √4√10
But hang on, √4 is actually 2, so √40 = 2√10
so 3√40 is 3 x 2√10 = 6√10

And 90 has factors 9 x 10 so √90 = √9√10
But hang on, √9 is actually 3, so √9√10 = 3√10
so 6√90 is 6 x 3√10 = 18√10

so 3√40 + 6√90 = 6√10 + 18√10
= 24√10

Idk about psi but..

3 sqrt 40 + 6 sqrt 90

You basically have to break them down: 3 sqrt (2^2*5*2) + 6 sqrt (3^2*2*5)

Then 3*2 sqrt (10) + 6*3 sqrt (10)

since they both have sqrt (10), just combine. Remember PEMDAS

6+18=24 sqrt (10) =75.89

doubled check with a calc.

3√40+6√90

Take 3 inside the SQRT
= SQRT( 40 * 3*3) ............. once 3 goes inside the SQRT sign it doubles ( gets squared).
= SQRT(360)

Take 6 inside the SQRT
= SQRT( 90 * 6*6) ............. once 6 goes inside the SQRT sign it doubles ( gets squared).
= SQRT( 3240)

Now add them together
= SQRT( 360) + SQRT( 3240)
= SQRT( 3600)
= 60

3√40+6√90 =3√(4*10)+6√(9*10)= 3*2√10+6*3√10 = 6√10+18√10 = 24√10

3 [ 2√10 ] + 6 [ 3√10 ]

6√10 + 18√10

24√10