Simplify √ 45 to 3√ 5 and √ 28 to 2√ 7
Which gives you (3√5 +3√ 5 )+(−2√ 7 −2√ 7 )
Combine like terms = 6√ 5 −4√ 7
So the answer would be
6 square root of 5 end root minus 4 square root of 7
Hence, the simplified expression is:
6 square root of 5 end root minus 4 square root of 7.
i.e. [tex]6\sqrt{5}-4\sqrt{7}[/tex]
We are asked to simplify the expression:
3 square root of 5 end root minus 2 square root of 7 end root plus square root of 45 end root minus square root of 28.
which mathematically is given by:
[tex]3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}[/tex]
Since, we know that:
[tex]\sqrt[45}=\sqrt{3\times 3\times 5}\\\\i.e.\\\\\sqrt{45}=3\sqrt{5}[/tex]
and
[tex]\sqrt{28}=\sqrt{2\times 2\times 7}\\\\i.e.\\\\\sqrt{28}=2\sqrt{7}[/tex]
i.e. we need to simplify:
[tex]3\sqrt{5}-2\sqrt{7}+3\sqrt{5}-2\sqrt{7}[/tex]
Now, we combine the like terms as follows:
[tex]=3\sqrt{5}+3\sqrt{5}-2\sqrt{7}-2\sqrt{7}\\\\=6\sqrt{5}-4\sqrt{7}[/tex]
