diff --git a/mrbgems/mruby-bigint/core/bigint.c b/mrbgems/mruby-bigint/core/bigint.c
index abf8617eb..50fb42a32 100644
--- a/mrbgems/mruby-bigint/core/bigint.c
+++ b/mrbgems/mruby-bigint/core/bigint.c
@@ -1251,11 +1251,11 @@ mpz_bit_length(const mpz_t *x)
 {
   if (x->sz == 0 || x->sn == 0) return 0;
 
-  // 最上位 limb を取得（リトルエンディアン: 末尾）
+  // Get the most significant limb (last element in little-endian order)
   size_t i = x->sz - 1;
   mp_limb high = x->p[i];
 
-  // high の中で最上位のビットを探す
+  // Count the number of bits in the most significant limb
   size_t bits = 0;
   while (high != 0) {
     high >>= 1;
@@ -1277,7 +1277,7 @@ mpz_sqrt(mrb_state *mrb, mpz_t *z, mpz_t *x)
     return;
   }
 
-  // 初期値の設定: bit-length の半分の位置に 1 を立てる
+  // Estimate initial value: 1 << (bit_length(x) / 2)
   size_t xbits = mpz_bit_length(x);
   size_t sbit = (xbits + 1) / 2;
   mpz_t s, t;
@@ -1286,14 +1286,16 @@ mpz_sqrt(mrb_state *mrb, mpz_t *z, mpz_t *x)
 
   mpz_init(mrb, &t);
 
-  // ループ: s = (s + x / s) / 2
+  // Iteratively refine s using Newton-Raphson method:
+  // s = (s + x / s) / 2
   for (;;) {
     mpz_mdiv(mrb, &t, x, &s);     // t = x / s
     mpz_add(mrb, &t, &t, &s);     // t = s + x/s
     mpz_div_2exp(mrb, &t, &t, 1); // t = (s + x/s) / 2
 
     if (mpz_cmp(mrb, &t, &s) >= 0) {
-      break; // 収束
+      // Converged: t >= s
+      break;
     }
 
     mpz_set(mrb, &s, &t);