Add. Write your answer in simplest form.
$8 \sqrt{63}+10 \sqrt{7}$
Answer (2)
Simplify 63 to 3 7 .
Rewrite the expression as 8 ( 3 7 ) + 10 7 .
Simplify the first term to 24 7 .
Combine like terms: 24 7 + 10 7 = 34 7 .
The final answer is 34 7 .
Explanation
Understanding the problem We are asked to add two terms involving square roots: 8 63 and 10 7 . To simplify the expression, we need to simplify the radicals and combine like terms.
Simplifying the radical First, we simplify 63 . We can factor 63 as 9 × 7 . Therefore, 63 = 9 × 7 = 9 × 7 = 3 7 .
Substituting the simplified radical Now we substitute this back into the original expression: 8 63 + 10 7 = 8 ( 3 7 ) + 10 7 .
Simplifying the expression Next, we simplify the first term: 8 ( 3 7 ) = 24 7 .
Combining like terms Now we combine like terms: 24 7 + 10 7 = ( 24 + 10 ) 7 .
Final calculation Finally, we add the numbers: ( 24 + 10 ) 7 = 34 7 .
Examples
Square roots are used in many areas of math and science. For example, when calculating the distance between two points in a coordinate plane, we use the distance formula, which involves square roots. Also, when dealing with right triangles and the Pythagorean theorem ( a 2 + b 2 = c 2 ), we often need to find the square root of a number to determine the length of a side. Simplifying radical expressions helps in obtaining exact values in these calculations.
To simplify the expression 8 63 + 10 7 , first simplify 63 to get 3 7 , leading to the expression 24 7 + 10 7 . Combining these gives 34 7 as the final answer. Therefore, the answer is 34 7 .
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