문제 은행 · 기초 수학 · 중학 수학 · 수와 연산

근호를 포함한 식의 계산

근호가 있는 식의 곱셈·나눗셈·분모의 유리화와 덧셈·뺄셈을 계산한다

유형전체 개념 확인 계산 그래프·표 해석 활용 증명·논술

난이도전체 기본 보통 도전

풀이전체 우리말 풀이 있는 문제만

유형·난이도는 우리말 풀이가 붙은 문제는 선생님이 정했고, 나머지는 자동 분류라 다를 수 있어요. 난이도가 정해지지 않은 문제는 난이도로 거를 때 빠집니다.

827문제 · 23 / 42쪽

441.OpenStax Elementary Algebra · 9.5절 · 8번우리말 번역

간단히 하세요: $-\frac{8}{3\sqrt{6}}$ .

영어 원문 보기

Simplify: $-\frac{8}{3\sqrt{6}}$ .

정답·풀이 보기

분모에서 제곱근을 없애기 위해 분모에 그 자신을 곱한다. 분수의 값이 변하지 않도록 분자와 분모에 모두 $\sqrt{6}$ 을 곱한다.



분자와 분모에 모두 $\sqrt{6}$ 을 곱한다.
간단히 한다.
공약수를 약분한다.
간단히 한다.

원본 교재 풀이(영어)

To remove the square root from the denominator, we multiply it by itself. To keep the fractions equivalent, we multiply both the numerator and denominator by $\sqrt{6}$ .


	$A mathematical expression displaying a fraction with a negative sign, where the numerator is 8 and the denominator is 3 multiplied by the square root of 6, represented as -8 / (3sqrt(6)).$
Multiply both the numerator and the denominator by $\sqrt{6}$ .
Simplify.	$A mathematical expression showing a negative fraction: - (8 times the square root of 6) divided by (3 multiplied by 6).$
Remove common factors.	$A mathematical expression showing a negative fraction where the factor 2 is crossed out in both the numerator and denominator. The numerator is 4 times the cancelled 2 times the square root of 6, and the denominator is 3 times the cancelled 2 times 3.$
Simplify.

한 번 더 — 비슷한 문제 풀기OpenStax Elementary Algebra · 9.2절 · 10번



이 분수는 완전제곱수가 아니므로 몫의 성질을 이용하여 다시 쓴다.
분모를 간단히 한다.
분모를 유리화한다.
간단히 한다.
간단히 한다.


	$A mathematical expression displays the square root of the fraction 5/12, with the numerator 5 and the denominator 12 clearly visible under the radical symbol.$
The fraction is not a perfect square, so rewrite using the Quotient Property.
Simplify the denominator	$A mathematical fraction with the square root of 5 in the numerator and 2 times the square root of 3 in the denominator.$
Rationalize the denominator.
Simplify.	$A mathematical fraction with the square root of 15 in the numerator and 2 multiplied by 3 in the denominator.$
Simplify.



몫의 성질을 사용하여 다시 쓴다.
분모를 간단히 한다.
분모를 유리화한다.
간단히 한다.
간단히 한다.


	$A mathematical expression showing the square root of the fraction 11 over 28.$
Rewrite using the Quotient Property.	$A mathematical expression showing the square root of 11 divided by the square root of 28, presented as a fraction.$
Simplify the denominator.
Rationalize the denominator.
Simplify.
Simplify.



분자와 분모에 분모의 켤레를 곱한다.
분모에서 켤레끼리 곱한다.
분모를 간단히 한다.
분모를 간단히 한다.
분자와 분모의 공약수를 약분한다.
분모를 간단히 한 뒤 공약수를 찾기 쉽도록 분자는 인수분해된 꼴로 둔다.


	$A fraction with 4 in the numerator and 4 + square root of 2 in the denominator.$
Multiply the numerator and denominator by the conjugate of the denominator.	$A mathematical expression showing the fraction 4(4-sqrt(2)) divided by the product of (4+sqrt(2)) and (4-sqrt(2)), with (4-sqrt(2)) highlighted in red in both the numerator and denominator.$
Multiply the conjugates in the denominator.	$A mathematical fraction is shown. The numerator is 4(4 - square root of 2). The denominator is 4 squared - (square root of 2) squared.$
Simplify the denominator.	$A mathematical expression showing a fraction. The numerator is 4(4 - square root of 2), and the denominator is 16 - 2.$
Simplify the denominator.	$A mathematical expression showing the fraction 4 multiplied by (4 minus the square root of 2), all divided by 14.$
Remove common factors from the numerator and denominator.	$A mathematical expression representing the fraction 2 multiplied by the quantity 4 minus the square root of 2, all divided by 7.$
We leave the numerator in factored form to make it easier to look for common factors after we have simplified the denominator.


	$A mathematical fraction is displayed, with 5 as the numerator and (2 - sqrt(3)) as the denominator. This represents the expression 5 / (2 minus the square root of 3).$
Multiply the numerator and denominator by the conjugate of the denominator.	$A fraction: 5(2 + sqrt(3)) / ((2 - sqrt(3))(2 + sqrt(3))). The common term (2 + sqrt(3)) is highlighted in red in both the numerator and denominator, indicating a step in simplification.$
Multiply the conjugates in the denominator.	$A mathematical expression showing a fraction. The numerator is 5 times (2 plus the square root of 3). The denominator is 2 squared minus the square root of 3 squared.$
Simplify the denominator.	$A mathematical expression showing a fraction with 5 multiplied by (2 plus the square root of 3) in the numerator, and (4 minus 3) in the denominator, on a white background.$
Simplify the denominator.	$A mathematical expression showing the fraction 5(2 + 3)/1.$
Simplify.


	$A mathematical expression showing a fraction with the square root of 3 in the numerator and the square root of u minus the square root of 6 in the denominator.$
Multiply the numerator and denominator by the conjugate of the denominator.	$A fraction with a square root of three times the quantity of the square root of u plus the square root of six in the numerator. The denominator is the product of the quantity of the square root of u minus the square root of six and the quantity of the square root of u plus the square root of six.$
Multiply the conjugates in the denominator.	$A mathematical expression showing the fraction: square root of 3 multiplied by the sum of square root of 'u' and square root of 6, all divided by 'u' minus 6.$
Simplify the denominator.	$A fraction with a numerator of 'square root 3 times the quantity square root u plus square root 6' and a denominator of 'u minus 6'.$


	$A mathematical fraction is displayed, with the numerator as the square root of x plus the square root of 7, and the denominator as the square root of x minus the square root of 7.$
Multiply the numerator and denominator by the conjugate of the denominator.	$An algebraic fraction showing (sqrt(x)+sqrt(7))^2 divided by (sqrt(x)-sqrt(7))(sqrt(x)+sqrt(7)), illustrating a step in simplifying radical expressions.$
Multiply the conjugates in the denominator.	$A mathematical fraction with the numerator as the product of (square root x + square root 7) and (square root x + square root 7), and the denominator as (square root x) squared minus (square root 7) squared.$
Simplify the denominator.	$A fraction with numerator (sqrt(x) + sqrt(7))^2 and denominator (x - 7).$
We do not square the numerator. In factored form, we can see there are no common factors to remove from the numerator and denominator.