Answer:
The answer is
[tex]43 \sqrt{10} [/tex]
Step-by-step explanation:
[tex]5 \sqrt{490} + 4 \sqrt{40} [/tex]
First of all we must make sure that the surds have equal roots
For 5√490
[tex]5 \sqrt{490} = 5 \sqrt{49 \times 10 } \\ = 5 \times \sqrt{49} \times \sqrt{10} \\ = 5 \times 7 \sqrt{10} \\ = 35 \sqrt{10} [/tex]
For 4√40
[tex]4 \sqrt{40} = 4 \times \sqrt{4 \times 10} \\ = 4 \times \sqrt{4} \times \sqrt{10} \\ = 4 \times 2 \sqrt{10} \\ = 8 \sqrt{10} [/tex]
So we have
[tex]35 \sqrt{10} + 8 \sqrt{10} [/tex]
Using the rules of surds simplify the expression
That's
[tex]a \sqrt{x} + b \sqrt{x} = (a + b) \sqrt{x} [/tex]
So we have
[tex]35 \sqrt{10} + 8 \sqrt{10} = (35 + 8) \sqrt{10} \\ [/tex]
We have the final answer as
[tex]43 \sqrt{10} [/tex]
Hope this helps you
