Final answer:
Simplify the expression by finding perfect squares that are factors of the numbers under the square root. Simplify √8 to 2√2 and √50 to 5√2, then combine like terms to get 7√2. Leave √7 as is to get the final simplified expression, 7√2 + √7.
Step-by-step explanation:
When simplifying the expression root of 8 + root of 50 + root of 7, we are dealing with the simplification of square roots. The square root of a number is the same as the number raised to the power of 0.5. Our current expression involves square roots of several numbers.
First, we look for perfect squares that are factors of the numbers under the square root to simplify the expression. For example:
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- The square root of 8 can be simplified by recognizing that 8 is 4 times 2, and 4 is a perfect square. Hence, √8 = √(4×2) = √4 × √2 = 2√2.
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- The square root of 50 works similarly since 50 is 25 times 2, and 25 is a perfect square. So, √50 = √(25×2) = √25 × √2 = 5√2.
There is no simplification for √7 since 7 is a prime number and doesn't have perfect square factors other than 1.
Combining our simplified terms, we have: 2√2 + 5√2 + √7. Since 2√2 and 5√2 have the same radical part, we can add them like like terms. This gives us (2+5)√2 or 7√2.
Adding √7, which cannot be combined with 7√2, we leave as is.
Therefore, the simplified expression is 7√2 + √7.
It's important to always eliminate terms wherever possible to simplify the algebra, and after doing so, check the answer to see if it is reasonable. This is in accordance with mathematical properties such as manipulating exponents or reducing fractions by common factors.