How many integers are between 5 roots of 7 and 7 roots of 5?

Question

Cameron Benitez · Accepted Answer

To answer the question of the problem, you need to add the factors before the root under the root sign, then find between these numbers such numbers from which the root is extracted (that is, numbers that are perfect squares) and count the number of these numbers:

5 \sqrt{7} = \sqrt{5^{2} * 7} = \sqrt{25 * 7} = \sqrt{175}

7 \sqrt{5} = \sqrt{7^{2} * 5} = \sqrt{49 * 5} = \sqrt{245}

Between the numbers 175 and 245 are the numbers

196 = 14^{2}

and

225 = 15^{2}

, i.e. between the numbers

5 \sqrt{7}

and

7 \sqrt{5}

there are only two integers.
Answer: 2.

incibracy5x · Accepted Answer

Answer:Between these roots lie two integers 14 and 15.Step by step explanation:Let&#039;s introduce the coefficients under the roots.  5      7    =      25    ∗    7    =      175    7      5    =      49    ∗    5    =      245  Between these numbers there are two integers       196    =  14 and       225    =  15

How many integers are between 5 roots of 7 and 7 roots of 5?

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