Math problem: 10th root of 3 + sqrt of 3 Simplify?

Question

how can I simplify this?

(10th root of 3) + (sqrt of 3)
which is equal to
3 to the power of 1/10 + 3 to the power of 1/2

Answer 1

3^(1/10) + 3^(1/2)

One thing you can try to do is decompose 1/10 into 1/5 times 1/2.

3^([1/5] * [1/2]) + 3^(1/2)

Remember that a^(bc) can be expressed as (a^b)^c.

[3^(1/2)]^(1/5) + 3^(1/2)

There's really nothing much you can do to simpilfy this.

Answer 2

So far, you have....

3^(1/10) + 3^(1/2)

First: when you have the same base, in this case the base is "3," you add the exponents....

3^(1/10 + 1/2)

3^(3/5)

Sec: rewrite the expression in the radical form > the 5th root of 3^3....

V`(3^3)

Third: rewrite the expression in lowest terms > find the 5th root of 3^3.....

V`(3*3*3)

3V`3

Or, 3^(1/3)

Answer 3

3^(1/10)+3^(1/2)
=3^[(1/10)+(1/2)]
=3^[(1+5)/10]
=3^(6/10)
=3^(3/5)