 # How many integers are between 5 roots of 7 and 7 roots of 5? Ciolan3u 2022-09-14 Answered
How many integers are between 5 roots of 7 and 7 roots of 5?
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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:
$5\sqrt{7}=\sqrt{{5}^{2}\ast 7}=\sqrt{25\ast 7}=\sqrt{175}$
$7\sqrt{5}=\sqrt{{7}^{2}\ast 5}=\sqrt{49\ast 5}=\sqrt{245}$
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.
###### Not exactly what you’re looking for? incibracy5x
Between these roots lie two integers 14 and 15.
Step by step explanation:
Let's introduce the coefficients under the roots.
$5\sqrt{7}=\sqrt{25\ast 7}=\sqrt{175}$
$7\sqrt{5}=\sqrt{49\ast 5}=\sqrt{245}$
Between these numbers there are two integers $\sqrt{196}=14$ and $\sqrt{225}=15$