پلانز

جذر المربع کیلکولیٹر اور جذر سادہ کرنے والا

65 کا جذر المربع کیا ہے؟ √65 ≈ 8.062258، اور یہ سادہ نہیں ہو سکتا کیونکہ 65 کا کوئی مربع جزو ضربی نہیں۔ یہ کیلکولیٹر کوئی بھی جذر نکالتا ہے اور اسے سادہ ترین جذری صورت میں لکھتا ہے، جیسے √180 = 6√5۔

مکمل اعداد، اعشاریے یا 2/3 جیسی کسور

نتیجہ

قدریں درج کریں اور نتیجہ دیکھنے کے لیے “حساب کریں” دبائیں۔

فارمولا

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.

یہ کیلکولیٹر کیسے استعمال کریں

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

حل شدہ مثالیں

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.

عام غلطیاں

  • 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.

اکثر پوچھے گئے سوالات

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.

مزید جانیں