الخطط

حاسبة الجذر التربيعي وتبسيط الجذور

ما الجذر التربيعي لـ 65؟ √65 ≈ 8.062258، ولا يمكن تبسيطه لأن 65 ليس له عامل مربع. تجد هذه الحاسبة أي جذر وتكتبه في أبسط صورة جذرية، مثل √180 = 6√5.

أعداد صحيحة أو عشرية أو كسور مثل 2/3

النتيجة

أدخل القيم واضغط احسب لرؤية النتيجة.

الصيغة

a2b=ab\sqrt{a^2 b} = a\sqrt{b}

Take square factors out of the root: √72 = √(36 × 2) = 6√2.

anbn=abn\sqrt[n]{a^n b} = a\sqrt[n]{b}

For an nth root, take out factors that are perfect nth powers.

كيفية استخدام هذه الحاسبة

  1. Enter the number and choose which root you want.
  2. Press Calculate to get the simplified exact root and its decimal value.

أمثلة محلولة

The square root of 72

72 = 36 × 2, and 36 = 6² is a perfect square.

√72 = √(6² × 2) = 6√2 ≈ 8.485281.

The square root of 65

65 = 5 × 13. Neither factor is a perfect square, so √65 is already in simplest radical form.

√65 lies between √64 = 8 and √81 = 9, very close to 8: √65 ≈ 8.062258.

Simplify a cube root: ∛54

Choose the cube root. 54 = 27 × 2, and 27 = 3³ is a perfect cube.

∛54 = ∛27 × ∛2 = 3∛2 ≈ 3.779763.

أخطاء شائعة

  • Not using the largest square factor: √180 = 2√45 is true but unfinished — 45 still contains 9. The simplest form is 6√5.
  • Splitting a sum: √(9 + 16) is 5, not √9 + √16 = 7.
  • Treating the decimal as exact: √65 ≈ 8.062258 is rounded; √65 is the exact value.

الأسئلة الشائعة

How do you simplify √180?

180 = 36 × 5, so √180 = 6√5 ≈ 13.416408 in simplest radical form.

What is the square root of 2116?

46, because 46 × 46 = 2116. It is a perfect square, so the root is a whole number.

What is the square root of x⁶?

√(x⁶) = |x³|, because (x³)² = x⁶. For x ≥ 0 that is simply x³. This calculator works with numbers; the algebra calculator handles expressions with letters.

Why is the answer written as 6√2 instead of a decimal?

√2 never ends or repeats, so 6√2 is the exact answer. The decimal shown with it is rounded.

Can I take the root of a negative number?

Odd roots, yes: ∛(−27) = −3. Even roots (square, 4th, …) of a negative number are not real numbers.

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