add root 3 + 7 root 5 and 4 root 3 + 6 root 5
Answers
Answer:
37.724 is the answer for your question
Answer:
Simplify: \mathbf{\color{green}{ 2\,\sqrt{3\,} + 3\,\sqrt{3\,} }}2
3
+3
3
Since the radical is the same in each term (being the square root of three), then these are "like" terms. This means that I can combine the terms.
Step-by-step explanation:
have two copies of the radical, added to another three copies. This gives mea total of five copies:
2\,\sqrt{3\,} + 3\,\sqrt{3\,} = (2 + 3)\,\sqrt{3\,}2
3
+3
3
=(2+3)
3
= \mathbf{\color{purple}{ 5\,\sqrt{3\,} }}=5
3
That middle step, with the parentheses, shows the reasoning that justifies the final answer. You probably won't ever need to "show" this step, but it's what should be going through your mind.
Simplify: \mathbf{\color{green}{ \sqrt{3\,} + 4\,\sqrt{3\,} }}
3
+4
3
The radical part is the same in each term, so I can do this addition. To help me keep track that the first term means "one copy of the square root of three", I'll insert the "understood" "1":
\sqrt{3\,} + 4\,\sqrt{3\,} = 1\,\sqrt{3\,} + 4\,\sqrt{3\,}
3
+4
3
=1
3
+4
3
= (1 + 4)\,\sqrt{3\,}=(1+4)
3
= \mathbf{\color{purple}{ 5\,\sqrt{3\,} }}=5
3
Don't assume that expressions with unlike radicals cannot be simplified. It is possible that, after simplifying the radicals, the expression can indeed be simplified.
Simplify: \mathbf{\color{green}{\sqrt{9\,} + \sqrt{25\,}}}
9
+
25
To simplify a radical addition, I must first see if I can simplify each radical term. In this particular case, the square roots simplify "completely" (that is, down to whole numbers):
\sqrt{9\,} + \sqrt{25\,} = 3 + 5 = \mathbf{\color{purple}{ 8 }}
9
+
25
=3+5=8
Simplify: \mathbf{\color{green}{ 3\,\sqrt{4\,} + 2\,\sqrt{4\,} }}3
4
+2
4
I have three copies of the radical, plus another two copies, giving me— Wait a minute! I can simplify those radicals right down to whole numbers:
3\,\sqrt{4\,} + 2\,\sqrt{4\,} = 3\times 2 + 2\times 23
4
+2
4
=3×2+2×2
= 6 + 4 = \mathbf{\color{purple}{ 10 }}=6+4=10
Don't worry if you don't see a simplification right away. If I hadn't noticed until the end that the radical simplified, my steps would have been different, but my final answer would have been the same:
3\,\sqrt{4\,} + 2\,\sqrt{4\,} = 5\,\sqrt{4\,}3
4
+2
4
=5
4
= 5\times 2 = 10=5×2=10